diff --git a/src/cairo-analysis-surface.c b/src/cairo-analysis-surface.c
index b3eab41f4..b80ad628c 100644
--- a/src/cairo-analysis-surface.c
+++ b/src/cairo-analysis-surface.c
@@ -481,7 +481,7 @@ _cairo_analysis_surface_stroke (void			*abstract_surface,
 	cairo_rectangle_int_t mask_extents;
 
 	_cairo_path_fixed_approximate_stroke_extents (path,
-						      style, ctm, tolerance,
+						      style, ctm,
 						      &mask_extents);
 
 	is_empty = _cairo_rectangle_intersect (&extents, &mask_extents);
@@ -539,7 +539,6 @@ _cairo_analysis_surface_fill (void			*abstract_surface,
 	cairo_rectangle_int_t mask_extents;
 
 	_cairo_path_fixed_approximate_fill_extents (path,
-						    tolerance,
 						    &mask_extents);
 
 	is_empty = _cairo_rectangle_intersect (&extents, &mask_extents);
diff --git a/src/cairo-gstate.c b/src/cairo-gstate.c
index 9ebc5d17b..df7ec5c41 100644
--- a/src/cairo-gstate.c
+++ b/src/cairo-gstate.c
@@ -796,8 +796,7 @@ _cairo_gstate_path_extents (cairo_gstate_t     *gstate,
     double px1, py1, px2, py2;
 
     _cairo_path_fixed_bounds (path,
-			      &px1, &py1, &px2, &py2,
-			      gstate->tolerance);
+			      &px1, &py1, &px2, &py2);
 
     _cairo_gstate_backend_to_user_rectangle (gstate,
 					     &px1, &py1, &px2, &py2,
diff --git a/src/cairo-path-bounds.c b/src/cairo-path-bounds.c
index 698d1fa5b..56f2df52f 100644
--- a/src/cairo-path-bounds.c
+++ b/src/cairo-path-bounds.c
@@ -37,8 +37,6 @@
 #include "cairoint.h"
 
 typedef struct cairo_path_bounder {
-    double tolerance;
-
     cairo_point_t current_point;
     cairo_bool_t has_initial_point;
     cairo_bool_t has_point;
@@ -47,9 +45,8 @@ typedef struct cairo_path_bounder {
 } cairo_path_bounder_t;
 
 static void
-_cairo_path_bounder_init (cairo_path_bounder_t *bounder, double tolerance)
+_cairo_path_bounder_init (cairo_path_bounder_t *bounder)
 {
-    bounder->tolerance = tolerance;
     bounder->has_initial_point = FALSE;
     bounder->has_point = FALSE;
 }
@@ -167,7 +164,7 @@ _cairo_path_fixed_approximate_extents (cairo_path_fixed_t *path,
     cairo_path_bounder_t bounder;
     cairo_status_t status;
 
-    _cairo_path_bounder_init (&bounder, 0.);
+    _cairo_path_bounder_init (&bounder);
 
     status = _cairo_path_fixed_interpret (path, CAIRO_DIRECTION_FORWARD,
 					  _cairo_path_bounder_move_to,
@@ -192,13 +189,12 @@ _cairo_path_fixed_approximate_extents (cairo_path_fixed_t *path,
  */
 void
 _cairo_path_fixed_approximate_fill_extents (cairo_path_fixed_t *path,
-					    double tolerance,
 					    cairo_rectangle_int_t *extents)
 {
     cairo_path_bounder_t bounder;
     cairo_status_t status;
 
-    _cairo_path_bounder_init (&bounder, tolerance);
+    _cairo_path_bounder_init (&bounder);
 
     status = _cairo_path_fixed_interpret (path, CAIRO_DIRECTION_FORWARD,
 					  _cairo_path_bounder_move_to,
@@ -223,13 +219,12 @@ void
 _cairo_path_fixed_approximate_stroke_extents (cairo_path_fixed_t *path,
 					      cairo_stroke_style_t *style,
 					      const cairo_matrix_t *ctm,
-					      double tolerance,
 					      cairo_rectangle_int_t *extents)
 {
     cairo_path_bounder_t bounder;
     cairo_status_t status;
 
-    _cairo_path_bounder_init (&bounder, tolerance);
+    _cairo_path_bounder_init (&bounder);
 
     status = _cairo_path_fixed_interpret (path, CAIRO_DIRECTION_FORWARD,
 					  _cairo_path_bounder_move_to,
@@ -261,13 +256,12 @@ _cairo_path_fixed_approximate_stroke_extents (cairo_path_fixed_t *path,
 void
 _cairo_path_fixed_bounds (cairo_path_fixed_t *path,
 			  double *x1, double *y1,
-			  double *x2, double *y2,
-			  double tolerance)
+			  double *x2, double *y2)
 {
     cairo_path_bounder_t bounder;
     cairo_status_t status;
 
-    _cairo_path_bounder_init (&bounder, tolerance);
+    _cairo_path_bounder_init (&bounder);
 
     status = _cairo_path_fixed_interpret (path, CAIRO_DIRECTION_FORWARD,
 					  _cairo_path_bounder_move_to,
diff --git a/src/cairo-surface-fallback.c b/src/cairo-surface-fallback.c
index 9cd59d425..6cc67d190 100644
--- a/src/cairo-surface-fallback.c
+++ b/src/cairo-surface-fallback.c
@@ -958,7 +958,6 @@ _cairo_surface_fallback_fill (cairo_surface_t		*surface,
 	    cairo_rectangle_int_t path_extents;
 
 	    _cairo_path_fixed_approximate_fill_extents (path,
-							tolerance,
 							&path_extents);
 	    if (! _cairo_rectangle_intersect (&extents, &path_extents))
 		return CAIRO_STATUS_SUCCESS;
diff --git a/src/cairoint.h b/src/cairoint.h
index 95b5e0fa8..2a6681d08 100644
--- a/src/cairoint.h
+++ b/src/cairoint.h
@@ -1545,21 +1545,18 @@ _cairo_path_fixed_approximate_extents (cairo_path_fixed_t	*path,
 
 cairo_private void
 _cairo_path_fixed_approximate_fill_extents (cairo_path_fixed_t *path,
-					    double tolerance,
 					    cairo_rectangle_int_t *extents);
 
 cairo_private void
 _cairo_path_fixed_approximate_stroke_extents (cairo_path_fixed_t *path,
 					      cairo_stroke_style_t *style,
 					      const cairo_matrix_t *ctm,
-					      double tolerance,
 					      cairo_rectangle_int_t *extents);
 
 cairo_private void
 _cairo_path_fixed_bounds (cairo_path_fixed_t *path,
 			  double *x1, double *y1,
-			  double *x2, double *y2,
-			  double tolerance);
+			  double *x2, double *y2);
 
 cairo_private void
 _cairo_path_fixed_transform (cairo_path_fixed_t	*path,