diff --git i/lib/matplotlib/text.py w/lib/matplotlib/text.py
index b2b2195837..02f34ddf7e 100644
--- i/lib/matplotlib/text.py
+++ w/lib/matplotlib/text.py
@@ -62,23 +62,23 @@ def _get_textbox(text, renderer):
     # called within the _get_textbox. So, it would better to move this
     # function as a method with some refactoring of _get_layout method.
 
-    projected_xs = []
-    projected_ys = []
+    projected_xys = []
 
     theta = np.deg2rad(text.get_rotation())
     tr = Affine2D().rotate(-theta)
 
-    _, parts, d = text._get_layout(renderer)
+    _, parts, _ = text._get_layout(renderer)
 
-    for t, wh, x, y in parts:
-        w, h = wh
-
-        xt1, yt1 = tr.transform((x, y))
-        yt1 -= d
-        xt2, yt2 = xt1 + w, yt1 + h
-
-        projected_xs.extend([xt1, xt2])
-        projected_ys.extend([yt1, yt2])
+    for i, (t, wad, x, y) in enumerate(parts):
+        w, a, d = wad
+        xt, yt = tr.transform((x, y))
+        projected_xys.extend([
+            (xt, yt + a),
+            (xt, yt - d),
+            (xt + w, yt + a),
+            (xt + w, yt - d),
+        ])
+    projected_xs, projected_ys = zip(*projected_xys)
 
     xt_box, yt_box = min(projected_xs), min(projected_ys)
     w_box, h_box = max(projected_xs) - xt_box, max(projected_ys) - yt_box
@@ -300,8 +300,7 @@ class Text(Artist):
         thisx, thisy = 0.0, 0.0
         lines = self.get_text().split("\n")  # Ensures lines is not empty.
 
-        ws = []
-        hs = []
+        wads = []  # widths, ascents above baseline, descents below baseline.
         xs = []
         ys = []
 
@@ -309,7 +308,8 @@ class Text(Artist):
         _, lp_h, lp_d = renderer.get_text_width_height_descent(
             "lp", self._fontproperties,
             ismath="TeX" if self.get_usetex() else False)
-        min_dy = (lp_h - lp_d) * self._linespacing
+        lp_a = lp_h - lp_d  # ascent, i.e. height above-the-baseline.
+        min_dy = lp_a * self._linespacing
 
         for i, line in enumerate(lines):
             clean_line, ismath = self._preprocess_math(line)
@@ -318,26 +318,25 @@ class Text(Artist):
                     clean_line, self._fontproperties, ismath=ismath)
             else:
                 w = h = d = 0
-
-            # For multiline text, increase the line spacing when the text
-            # net-height (excluding baseline) is larger than that of a "l"
-            # (e.g., use of superscripts), which seems what TeX does.
-            h = max(h, lp_h)
+            a = h - d
+            # Pretend that the ascent of all lines is at least as large as "l",
+            # to ensure good linespacing.  This seems similar to what TeX does.
+            a = max(a, lp_a)
+            # Pretend that the descent of all lines is at least as large as
+            # "p", to ensure good linespacing.
             d = max(d, lp_d)
+            # Ideally, a should not be adjusted on the first line and d should
+            # not be adjusted on the last line (they don't participate in
+            # linespacing), but this would break all baseline images.
 
-            ws.append(w)
-            hs.append(h)
+            baseline = a - thisy  # Last line metrics; needed later.
 
-            # Metrics of the last line that are needed later:
-            baseline = (h - d) - thisy
-
-            if i == 0:
-                # position at baseline
-                thisy = -(h - d)
-            else:
-                # put baseline a good distance from bottom of previous line
-                thisy -= max(min_dy, (h - d) * self._linespacing)
+            if i == 0:  # position at baseline
+                thisy = -a
+            else:  # put baseline a good distance from bottom of previous line
+                thisy -= max(min_dy, a * self._linespacing)
 
+            wads.append((w, a, d))
             xs.append(thisx)  # == 0.
             ys.append(thisy)
 
@@ -347,6 +346,7 @@ class Text(Artist):
         descent = d
 
         # Bounding box definition:
+        ws = [w for w, a, d in wads]
         width = max(ws)
         xmin = 0
         xmax = width
@@ -440,7 +440,7 @@ class Text(Artist):
         # now rotate the positions around the first (x, y) position
         xys = M.transform(offset_layout) - (offsetx, offsety)
 
-        ret = bbox, list(zip(lines, zip(ws, hs), *xys.T)), descent
+        ret = bbox, list(zip(lines, wads, *xys.T)), descent
         self._cached[key] = ret
         return ret
 
@@ -709,7 +709,7 @@ class Text(Artist):
 
             angle = self.get_rotation()
 
-            for line, wh, x, y in info:
+            for line, wad, x, y in info:
 
                 mtext = self if len(info) == 1 else None
                 x = x + posx