diff --git a/doc/api/lines_api.rst b/doc/api/lines_api.rst
index 808df726d118..94af43cf6feb 100644
--- a/doc/api/lines_api.rst
+++ b/doc/api/lines_api.rst
@@ -17,6 +17,7 @@ Classes
 
    Line2D
    VertexSelector
+   Line2DWithErrorbars
 
 Functions
 ---------
@@ -26,4 +27,3 @@ Functions
    :template: autosummary.rst
 
    segment_hits
-   
\ No newline at end of file
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 35fd2b0ce890..ea21a75eb716 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -3211,7 +3211,8 @@ def errorbar(self, x, y, yerr=None, xerr=None,
         `.ErrorbarContainer`
             The container contains:
 
-            - plotline: `.Line2D` instance of x, y plot markers and/or line.
+            - plotline: `.Line2DWithErrorbars` instance of x, y plot markers
+              and/or line.
             - caplines: A tuple of `.Line2D` instances of the error bar caps.
             - barlinecols: A tuple of `.LineCollection` with the horizontal and
               vertical error ranges.
@@ -3239,7 +3240,6 @@ def errorbar(self, x, y, yerr=None, xerr=None,
         # anything that comes in as 'None', drop so the default thing
         # happens down stream
         kwargs = {k: v for k, v in kwargs.items() if v is not None}
-        kwargs.setdefault('zorder', 2)
 
         try:
             offset, errorevery = errorevery
@@ -3301,8 +3301,6 @@ def errorbar(self, x, y, yerr=None, xerr=None,
         plot_line_style = {
             **base_style,
             **kwargs,
-            'zorder': (kwargs['zorder'] - .1 if barsabove else
-                       kwargs['zorder'] + .1),
         }
 
         # make the style dict for the line collections (the bars)
@@ -3344,13 +3342,9 @@ def errorbar(self, x, y, yerr=None, xerr=None,
                 eb_cap_style[key] = kwargs[key]
         eb_cap_style['color'] = ecolor
 
-        data_line = None
-        if plot_line:
-            data_line = mlines.Line2D(x, y, **plot_line_style)
-            self.add_line(data_line)
-
-        barcols = []
-        caplines = []
+        eb_line = mlines.Line2DWithErrorbars(
+            x, y, barsabove=barsabove, plot_line=plot_line, **plot_line_style)
+        self.add_line(eb_line)
 
         # arrays fine here, they are booleans and hence not units
         lolims = np.broadcast_to(lolims, len(x)).astype(bool)
@@ -3408,6 +3402,92 @@ def extract_err(err, data):
             high = [v + e for v, e in zip(data, b)]
             return low, high
 
+        def eb_hlines(y, xmin, xmax, colors='k', linestyles='solid',
+                      label='', **kwargs):
+            """Private function like hlines, but not adding lines to Axes"""
+            self._process_unit_info([xmin, xmax], y, kwargs=kwargs)
+            y = self.convert_yunits(y)
+            xmin = self.convert_xunits(xmin)
+            xmax = self.convert_xunits(xmax)
+
+            if not np.iterable(y):
+                y = [y]
+            if not np.iterable(xmin):
+                xmin = [xmin]
+            if not np.iterable(xmax):
+                xmax = [xmax]
+
+            # Create and combine masked_arrays from input
+            y, xmin, xmax = cbook._combine_masks(y, xmin, xmax)
+            y = np.ravel(y)
+            xmin = np.ravel(xmin)
+            xmax = np.ravel(xmax)
+
+            masked_verts = np.ma.empty((len(y), 2, 2))
+            masked_verts[:, 0, 0] = xmin
+            masked_verts[:, 0, 1] = y
+            masked_verts[:, 1, 0] = xmax
+            masked_verts[:, 1, 1] = y
+
+            if len(y) > 0:
+                minx = min(xmin.min(), xmax.min())
+                maxx = max(xmin.max(), xmax.max())
+                miny = y.min()
+                maxy = y.max()
+
+                corners = (minx, miny), (maxx, maxy)
+                self.update_datalim(corners)
+                self._request_autoscale_view()
+
+            lines = mcoll.LineCollection(masked_verts, colors=colors,
+                                         linestyles=linestyles, label=label)
+            lines.update(kwargs)
+            return lines
+
+        def eb_vlines(x, ymin, ymax, colors='k', linestyles='solid',
+                      label='', **kwargs):
+            """Private function like vlines, but not adding lines to Axes"""
+            self._process_unit_info(xdata=x, ydata=[ymin, ymax], kwargs=kwargs)
+
+            # We do the conversion first since not all unitized data is uniform
+            x = self.convert_xunits(x)
+            ymin = self.convert_yunits(ymin)
+            ymax = self.convert_yunits(ymax)
+
+            if not np.iterable(x):
+                x = [x]
+            if not np.iterable(ymin):
+                ymin = [ymin]
+            if not np.iterable(ymax):
+                ymax = [ymax]
+
+            # Create and combine masked_arrays from input
+            x, ymin, ymax = cbook._combine_masks(x, ymin, ymax)
+            x = np.ravel(x)
+            ymin = np.ravel(ymin)
+            ymax = np.ravel(ymax)
+
+            masked_verts = np.ma.empty((len(x), 2, 2))
+            masked_verts[:, 0, 0] = x
+            masked_verts[:, 0, 1] = ymin
+            masked_verts[:, 1, 0] = x
+            masked_verts[:, 1, 1] = ymax
+
+            if len(x) > 0:
+                minx = x.min()
+                maxx = x.max()
+                miny = min(ymin.min(), ymax.min())
+                maxy = max(ymin.max(), ymax.max())
+
+                corners = (minx, miny), (maxx, maxy)
+                self.update_datalim(corners)
+                self._request_autoscale_view()
+
+            lines = mcoll.LineCollection(masked_verts, colors=colors,
+                                         linestyles=linestyles, label=label)
+            lines.update(kwargs)
+            return lines
+
         if xerr is not None:
             left, right = extract_err(xerr, x)
             # select points without upper/lower limits in x and
@@ -3416,46 +3496,46 @@ def extract_err(err, data):
             if noxlims.any() or len(noxlims) == 0:
                 yo, _ = xywhere(y, right, noxlims & everymask)
                 lo, ro = xywhere(left, right, noxlims & everymask)
-                barcols.append(self.hlines(yo, lo, ro, **eb_lines_style))
+                eb_line.add_barcols(eb_hlines(yo, lo, ro, **eb_lines_style))
                 if capsize > 0:
-                    caplines.append(mlines.Line2D(lo, yo, marker='|',
-                                                  **eb_cap_style))
-                    caplines.append(mlines.Line2D(ro, yo, marker='|',
-                                                  **eb_cap_style))
+                    eb_line.add_caplines(mlines.Line2D(lo, yo, marker='|',
+                                                       **eb_cap_style))
+                    eb_line.add_caplines(mlines.Line2D(ro, yo, marker='|',
+                                                       **eb_cap_style))
 
             if xlolims.any():
                 yo, _ = xywhere(y, right, xlolims & everymask)
                 lo, ro = xywhere(x, right, xlolims & everymask)
-                barcols.append(self.hlines(yo, lo, ro, **eb_lines_style))
+                eb_line.add_barcols(eb_hlines(yo, lo, ro, **eb_lines_style))
                 rightup, yup = xywhere(right, y, xlolims & everymask)
                 if self.xaxis_inverted():
                     marker = mlines.CARETLEFTBASE
                 else:
                     marker = mlines.CARETRIGHTBASE
-                caplines.append(
+                eb_line.add_caplines(
                     mlines.Line2D(rightup, yup, ls='None', marker=marker,
                                   **eb_cap_style))
                 if capsize > 0:
                     xlo, ylo = xywhere(x, y, xlolims & everymask)
-                    caplines.append(mlines.Line2D(xlo, ylo, marker='|',
-                                                  **eb_cap_style))
+                    eb_line.add_caplines(mlines.Line2D(xlo, ylo, marker='|',
+                                                       **eb_cap_style))
 
             if xuplims.any():
                 yo, _ = xywhere(y, right, xuplims & everymask)
                 lo, ro = xywhere(left, x, xuplims & everymask)
-                barcols.append(self.hlines(yo, lo, ro, **eb_lines_style))
+                eb_line.add_barcols(eb_hlines(yo, lo, ro, **eb_lines_style))
                 leftlo, ylo = xywhere(left, y, xuplims & everymask)
                 if self.xaxis_inverted():
                     marker = mlines.CARETRIGHTBASE
                 else:
                     marker = mlines.CARETLEFTBASE
-                caplines.append(
+                eb_line.add_caplines(
                     mlines.Line2D(leftlo, ylo, ls='None', marker=marker,
                                   **eb_cap_style))
                 if capsize > 0:
                     xup, yup = xywhere(x, y, xuplims & everymask)
-                    caplines.append(mlines.Line2D(xup, yup, marker='|',
-                                                  **eb_cap_style))
+                    eb_line.add_caplines(mlines.Line2D(xup, yup, marker='|',
+                                                       **eb_cap_style))
 
         if yerr is not None:
             lower, upper = extract_err(yerr, y)
@@ -3465,52 +3545,64 @@ def extract_err(err, data):
             if noylims.any() or len(noylims) == 0:
                 xo, _ = xywhere(x, lower, noylims & everymask)
                 lo, uo = xywhere(lower, upper, noylims & everymask)
-                barcols.append(self.vlines(xo, lo, uo, **eb_lines_style))
+                eb_line.add_barcols(eb_vlines(xo, lo, uo, **eb_lines_style))
                 if capsize > 0:
-                    caplines.append(mlines.Line2D(xo, lo, marker='_',
-                                                  **eb_cap_style))
-                    caplines.append(mlines.Line2D(xo, uo, marker='_',
-                                                  **eb_cap_style))
+                    eb_line.add_caplines(mlines.Line2D(xo, lo, marker='_',
+                                                       **eb_cap_style))
+                    eb_line.add_caplines(mlines.Line2D(xo, uo, marker='_',
+                                                       **eb_cap_style))
 
             if lolims.any():
                 xo, _ = xywhere(x, lower, lolims & everymask)
                 lo, uo = xywhere(y, upper, lolims & everymask)
-                barcols.append(self.vlines(xo, lo, uo, **eb_lines_style))
+                eb_line.add_barcols(eb_vlines(xo, lo, uo, **eb_lines_style))
                 xup, upperup = xywhere(x, upper, lolims & everymask)
                 if self.yaxis_inverted():
                     marker = mlines.CARETDOWNBASE
                 else:
                     marker = mlines.CARETUPBASE
-                caplines.append(
+                eb_line.add_caplines(
                     mlines.Line2D(xup, upperup, ls='None', marker=marker,
                                   **eb_cap_style))
                 if capsize > 0:
                     xlo, ylo = xywhere(x, y, lolims & everymask)
-                    caplines.append(mlines.Line2D(xlo, ylo, marker='_',
-                                                  **eb_cap_style))
+                    eb_line.add_caplines(mlines.Line2D(xlo, ylo, marker='_',
+                                                       **eb_cap_style))
 
             if uplims.any():
                 xo, _ = xywhere(x, lower, uplims & everymask)
                 lo, uo = xywhere(lower, y, uplims & everymask)
-                barcols.append(self.vlines(xo, lo, uo, **eb_lines_style))
+                eb_line.add_barcols(eb_vlines(xo, lo, uo, **eb_lines_style))
                 xlo, lowerlo = xywhere(x, lower, uplims & everymask)
                 if self.yaxis_inverted():
                     marker = mlines.CARETUPBASE
                 else:
                     marker = mlines.CARETDOWNBASE
-                caplines.append(
+                eb_line.add_caplines(
                     mlines.Line2D(xlo, lowerlo, ls='None', marker=marker,
                                   **eb_cap_style))
                 if capsize > 0:
                     xup, yup = xywhere(x, y, uplims & everymask)
-                    caplines.append(mlines.Line2D(xup, yup, marker='_',
-                                                  **eb_cap_style))
-        for l in caplines:
-            self.add_line(l)
+                    eb_line.add_caplines(mlines.Line2D(xup, yup, marker='_',
+                                                       **eb_cap_style))
+
+        for cl in eb_line._caplines:
+            self._update_line_limits(cl)
+            if cl.get_clip_path() is None:
+                cl.set_clip_path(self.patch)
+            if cl.mouseover:
+                self._mouseover_set.add(cl)
+        for bc in eb_line._barcols:
+            if bc.get_clip_path() is None:
+                bc.set_clip_path(self.patch)
+            if bc.mouseover:
+                self._mouseover_set.add(bc)
+        self.stale = True
 
         self._request_autoscale_view()
-        errorbar_container = ErrorbarContainer((data_line, tuple(caplines),
-                                                tuple(barcols)),
+        errorbar_container = ErrorbarContainer((eb_line if plot_line else None,
+                                                tuple(eb_line._caplines),
+                                                tuple(eb_line._barcols)),
                                                has_xerr=(xerr is not None),
                                                has_yerr=(yerr is not None),
                                                label=label)
diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
index c13cc16ea44e..8fa4b47dc793 100644
--- a/lib/matplotlib/lines.py
+++ b/lib/matplotlib/lines.py
@@ -1562,3 +1562,83 @@ def onpick(self, event):
 # You can not set the docstring of an instancemethod,
 # but you can on the underlying function.  Go figure.
 docstring.dedent_interpd(Line2D.__init__)
+
+
+class Line2DWithErrorbars(Line2D):
+    """
+    A helper class disguised as a `.Line2D` holding the errorbar elements.
+    """
+    def __init__(self, *args, barsabove=True, plot_line=True, **kwargs):
+        """
+        Create a `.Line2D`-like object holding all the `.Artists` required
+        to draw errorbars.
+
+        All `.Line2D` parameters are accepted. Additional parameters are:
+
+        barsabove: bool, optional
+            Specify the order errorbars are plot with respect to line markers.
+        plot_line:  bool, optional
+            Configure if line (and the respective markers) will be displayed.
+        """
+        super().__init__(*args, **kwargs)
+        self._barcols = []
+        self._caplines = []
+        self._barsabove = barsabove
+        self._plot_line = plot_line
+
+    def _set_artist_props(self, a):
+        """Set the boilerplate props for child artists."""
+        a.set_figure(self.figure)
+        if not a.is_transform_set():
+            a.set_transform(self.get_transform())
+        a.axes = self.axes
+
+    def _remove_caplines(self, caplines):
+        """Helper function to remove caplines, just for internal use."""
+        self._caplines.remove(caplines)
+        if (not self._caplines and not self._barcols and
+                not self._plot_line):
+            self.remove()
+
+    def _remove_barcols(self, barcols):
+        """Helper function to remove barcols, just for internal use."""
+        self._barcols.remove(barcols)
+        if (not self._caplines and not self._barcols and
+                not self._plot_line):
+            self.remove()
+
+    def add_caplines(self, caplines):
+        """Add a `.LineCollection` holding caplines information."""
+        caplines._remove_method = self._remove_caplines
+        self._caplines.append(caplines)
+
+    def add_barcols(self, barcols):
+        """Add a `.Line2D` holding barcols information."""
+        barcols._remove_method = self._remove_barcols
+        self._barcols.append(barcols)
+
+    @allow_rasterization
+    def draw(self, renderer):
+        # docstring inherited
+        if self._barsabove:
+            if self._plot_line:
+                super().draw(renderer)
+            for c in self.get_children():
+                self._set_artist_props(c)
+                c.draw(renderer)
+        else:
+            for c in self.get_children():
+                self._set_artist_props(c)
+                c.draw(renderer)
+            if self._plot_line:
+                super().draw(renderer)
+
+    def get_children(self):
+        # docstring inherited
+        return [*self._barcols, *self._caplines]
+
+    def remove(self):
+        # docstring inherited
+        self._plot_line = False
+        if (not self._caplines and not self._barcols):
+            super().remove()
diff --git a/lib/matplotlib/tests/baseline_images/test_legend/fancy.pdf b/lib/matplotlib/tests/baseline_images/test_legend/fancy.pdf
index 7930f6d68249..228d4a135d35 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_legend/fancy.pdf and b/lib/matplotlib/tests/baseline_images/test_legend/fancy.pdf differ
diff --git a/lib/matplotlib/tests/baseline_images/test_legend/fancy.png b/lib/matplotlib/tests/baseline_images/test_legend/fancy.png
index aba46e19e727..31893198a378 100644
Binary files a/lib/matplotlib/tests/baseline_images/test_legend/fancy.png and b/lib/matplotlib/tests/baseline_images/test_legend/fancy.png differ
diff --git a/lib/matplotlib/tests/baseline_images/test_legend/fancy.svg b/lib/matplotlib/tests/baseline_images/test_legend/fancy.svg
index 427ab827f4a1..ebb150c3cf76 100644
--- a/lib/matplotlib/tests/baseline_images/test_legend/fancy.svg
+++ b/lib/matplotlib/tests/baseline_images/test_legend/fancy.svg
@@ -1,7 +1,7 @@
 <?xml version="1.0" encoding="utf-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
   "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Created with matplotlib (http://matplotlib.org/) -->
+<!-- Created with matplotlib (https://matplotlib.org/) -->
 <svg height="432pt" version="1.1" viewBox="0 0 576 432" width="576pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
  <defs>
   <style type="text/css">
@@ -38,191 +38,191 @@ C -2.000462 -1.161816 -2.236068 -0.593012 -2.236068 0
 C -2.236068 0.593012 -2.000462 1.161816 -1.581139 1.581139 
 C -1.161816 2.000462 -0.593012 2.236068 0 2.236068 
 z
-" id="m27675ac663" style="stroke:#000000;"/>
+" id="m55f30c0a34" style="stroke:#000000;"/>
     </defs>
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+  <clipPath id="p0b51b03837">
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diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 828cc1438be7..55df8c2067ad 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -3296,10 +3296,50 @@ def test_errorbar_offsets(fig_test, fig_ref):
                          capsize=4, c=color)
 
         # Using manual errorbars
-        # n.b. errorbar draws the main plot at z=2.1 by default
-        ax_ref.plot(x, y, c=color, zorder=2.1)
         ax_ref.errorbar(x[shift::4], y[shift::4], yerr[shift::4],
                         capsize=4, c=color, fmt='none')
+        ax_ref.plot(x, y, c=color)
+
+
+@check_figures_equal()
+def test_errorbar_default_order(fig_test, fig_ref):
+    # Now test default order of errorbars and plots.
+    x = list(range(5))
+    y1 = np.full(5, -5)
+    y2 = np.full(5, 0)
+    y3 = np.full(5, 5)
+
+    yerr = list(range(5))
+
+    ax_ref = fig_ref.subplots()
+    ax_ref.plot(x, y1, 'ro', markersize=60, zorder=2.12)
+    ax_ref.errorbar(x, y1, yerr=yerr, fmt='none', ecolor='k', zorder=2.13)
+    ax_ref.plot(x, y1, 'b.', markersize=20, zorder=2.15)
+
+    ax_ref.plot(x, y2, 'ro', markersize=60, zorder=2.22)
+    ax_ref.errorbar(x, y2, yerr=yerr, fmt='none', ecolor='k', zorder=2.23)
+    ax_ref.plot(x, y2, 'gs', markersize=40, zorder=2.24)
+    ax_ref.plot(x, y2, 'b.', markersize=20, zorder=2.25)
+
+    ax_ref.plot(x, y3, 'ro', markersize=60, zorder=2.32)
+    ax_ref.plot(x, y3, 'gs', markersize=40, zorder=2.33)
+    ax_ref.errorbar(x, y3, yerr=yerr, fmt='none', ecolor='k', zorder=2.34)
+    ax_ref.plot(x, y3, 'b.', markersize=20, zorder=2.35)
+
+    ax_test = fig_test.subplots()
+
+    ax_test.plot(x, y1, 'ro', markersize=60)
+    ax_test.errorbar(x, y1, yerr=yerr, fmt='none', ecolor='k')
+    ax_test.plot(x, y1, 'b.', markersize=20)
+
+    ax_test.plot(x, y2, 'ro', markersize=60)
+    ax_test.errorbar(x, y2, yerr=yerr, fmt='gs', ecolor='k', markersize=40)
+    ax_test.plot(x, y2, 'b.', markersize=20)
+
+    ax_test.plot(x, y3, 'ro', markersize=60)
+    ax_test.errorbar(x, y3, yerr=yerr, fmt='gs', ecolor='k', markersize=40,
+                     barsabove=True)
+    ax_test.plot(x, y3, 'b.', markersize=20)
 
 
 @image_comparison(['hist_stacked_stepfilled', 'hist_stacked_stepfilled'])
diff --git a/lib/matplotlib/tests/test_lines.py b/lib/matplotlib/tests/test_lines.py
index d66509b0ee78..f21088a50373 100644
--- a/lib/matplotlib/tests/test_lines.py
+++ b/lib/matplotlib/tests/test_lines.py
@@ -217,3 +217,36 @@ def test_marker_as_markerstyle():
 
     assert_array_equal(line2.get_marker().vertices, triangle1.vertices)
     assert_array_equal(line3.get_marker().vertices, triangle1.vertices)
+
+
+def test_lines_with_errorbars():
+    x = list(range(5))
+    y = np.zeros(5)
+    err = list(range(5))
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    line, caplines, barcols = ax.errorbar(x, y, yerr=err, xerr=err)
+
+    # check consistent data structure
+    assert len(caplines) == 4
+    assert len(barcols) == 2
+    ax_lines = ax.get_lines()
+    assert len(ax_lines) == 1
+    assert line == ax_lines[0]
+
+    # make sure line is still present
+    line.remove()
+    ax_lines = ax.get_lines()
+    assert len(ax_lines) == 1
+    assert line == ax_lines[0]
+
+    # remove elements
+    for cl in caplines:
+        cl.remove()
+    for bc in barcols:
+        bc.remove()
+
+    # now the line should be gone too
+    ax_lines = ax.get_lines()
+    assert len(ax_lines) == 0
diff --git a/setup.cfg.template b/setup.cfg.template
deleted file mode 100644
index 562544fb1e59..000000000000
--- a/setup.cfg.template
+++ /dev/null
@@ -1,37 +0,0 @@
-# Rename this file to setup.cfg to modify Matplotlib's build options.
-
-[egg_info]
-
-[libs]
-# By default, Matplotlib downloads and builds its own copy of FreeType, and
-# builds its own copy of Qhull.  You may set the following to True to instead
-# link against a system FreeType/Qhull.
-#system_freetype = False
-#system_qhull = False
-
-[packages]
-# There are a number of data subpackages from Matplotlib that are
-# considered optional. All except 'tests' data (meaning the baseline
-# image files) are installed by default, but that can be changed here.
-#tests = False
-#sample_data = True
-
-[gui_support]
-# Matplotlib supports multiple GUI toolkits, known as backends.
-# The MacOSX backend requires the Cocoa headers included with XCode.
-# You can select whether to build it by uncommenting the following line.
-# It is never built on Linux or Windows, regardless of the config value.
-#
-#macosx = True
-
-[rc_options]
-# User-configurable options
-#
-# Default backend, one of: Agg, Cairo, GTK3Agg, GTK3Cairo, MacOSX, Pdf, Ps,
-# Qt4Agg, Qt5Agg, SVG, TkAgg, WX, WXAgg.
-#
-# The Agg, Ps, Pdf and SVG backends do not require external dependencies.  Do
-# not choose MacOSX if you have disabled the relevant extension modules.  The
-# default is determined by fallback.
-#
-#backend = Agg