diff --git a/lib/matplotlib/markers.py b/lib/matplotlib/markers.py
index fea9150d1a71..a6588c7c67f5 100644
--- a/lib/matplotlib/markers.py
+++ b/lib/matplotlib/markers.py
@@ -277,13 +277,13 @@ def _set_pixel(self):
         # Ideally, you'd want -0.5, -0.5 here, but then the snapping
         # algorithm in the Agg backend will round this to a 2x2
         # rectangle from (-1, -1) to (1, 1).  By offsetting it
-        # slightly, we can force it to be (0, -1) to (1, 0), which
-        # both makes it only be a single pixel and places it correctly
-        # with 1-width stroking (i.e. the ticks).  This hack is the
-        # best of a number of bad alternatives, mainly because the
+        # slightly, we can force it to be (0, 0) to (1, 1), which both
+        # makes it only be a single pixel and places it correctly
+        # aligned to 1-width stroking (i.e. the ticks).  This hack is
+        # the best of a number of bad alternatives, mainly because the
         # backends are not aware of what marker is actually being used
         # beyond just its path data.
-        self._transform = Affine2D().translate(-0.49999, -0.50001)
+        self._transform = Affine2D().translate(-0.49999, -0.49999)
         self._snap_threshold = None
 
     def _set_point(self):
diff --git a/src/_backend_agg.cpp b/src/_backend_agg.cpp
index f7a986fc2f95..96a9402ac0a8 100644
--- a/src/_backend_agg.cpp
+++ b/src/_backend_agg.cpp
@@ -433,10 +433,10 @@ RendererAgg::set_clipbox(const Py::Object& cliprect, R& rasterizer)
     double l, b, r, t;
     if (py_convert_bbox(cliprect.ptr(), l, b, r, t))
     {
-        rasterizer.clip_box(std::max(int(mpl_round(l)), 0),
-                            std::max(int(height) - int(mpl_round(b)), 0),
-                            std::min(int(mpl_round(r)), int(width)),
-                            std::min(int(height) - int(mpl_round(t)), int(height)));
+        rasterizer.clip_box(std::max(int(floor(l - 0.5)), 0),
+                            std::max(int(floor(height - b - 0.5)), 0),
+                            std::min(int(floor(r - 0.5)), int(width)),
+                            std::min(int(floor(height - t - 0.5)), int(height)));
     }
     else
     {
@@ -650,7 +650,7 @@ RendererAgg::draw_markers(const Py::Tuple& args)
     // Deal with the difference in y-axis direction
     marker_trans *= agg::trans_affine_scaling(1.0, -1.0);
     trans *= agg::trans_affine_scaling(1.0, -1.0);
-    trans *= agg::trans_affine_translation(0.0, (double)height);
+    trans *= agg::trans_affine_translation(0.5, (double)height + 0.5);
 
     PathIterator       marker_path(marker_path_obj);
     transformed_path_t marker_path_transformed(marker_path, marker_trans);
@@ -736,8 +736,8 @@ RendererAgg::draw_markers(const Py::Tuple& args)
                     continue;
                 }
 
-                x = (double)(int)x;
-                y = (double)(int)y;
+                x = floor(x);
+                y = floor(y);
 
                 // Cull points outside the boundary of the image.
                 // Values that are too large may overflow and create
@@ -772,8 +772,8 @@ RendererAgg::draw_markers(const Py::Tuple& args)
                     continue;
                 }
 
-                x = (double)(int)x;
-                y = (double)(int)y;
+                x = floor(x);
+                y = floor(y);
 
                 // Cull points outside the boundary of the image.
                 // Values that are too large may overflow and create
diff --git a/src/path_converters.h b/src/path_converters.h
index c45ff862c6f6..faacf15ad924 100644
--- a/src/path_converters.h
+++ b/src/path_converters.h
@@ -494,8 +494,8 @@ class PathSnapper
         code = m_source->vertex(x, y);
         if (m_snap && agg::is_vertex(code))
         {
-            *x = mpl_round(*x) + m_snap_value;
-            *y = mpl_round(*y) + m_snap_value;
+            *x = floor(*x - m_snap_value) + m_snap_value;
+            *y = floor(*y - m_snap_value) + m_snap_value;
         }
         return code;
     }