diff --git a/modules/juce_graphics/geometry/juce_Path.cpp b/modules/juce_graphics/geometry/juce_Path.cpp
index 7eecd66218..a4ff1e178a 100644
--- a/modules/juce_graphics/geometry/juce_Path.cpp
+++ b/modules/juce_graphics/geometry/juce_Path.cpp
@@ -60,6 +60,9 @@ const float Path::quadMarker           = 100003.0f;
 const float Path::cubicMarker          = 100004.0f;
 const float Path::closeSubPathMarker   = 100005.0f;
 
+const float Path::defaultToleranceForTesting = 1.0f;
+const float Path::defaultToleranceForMeasurement = 0.6f;
+
 //==============================================================================
 Path::PathBounds::PathBounds() noexcept
     : pathXMin (0), pathXMax (0), pathYMin (0), pathYMax (0)
@@ -1060,7 +1063,7 @@ bool Path::contains (const Point<float> point, const float tolerance) const
     return contains (point.x, point.y, tolerance);
 }
 
-bool Path::intersectsLine (const Line<float>& line, const float tolerance)
+bool Path::intersectsLine (Line<float> line, const float tolerance)
 {
     PathFlatteningIterator i (*this, AffineTransform(), tolerance);
     Point<float> intersection;
@@ -1072,7 +1075,7 @@ bool Path::intersectsLine (const Line<float>& line, const float tolerance)
     return false;
 }
 
-Line<float> Path::getClippedLine (const Line<float>& line, const bool keepSectionOutsidePath) const
+Line<float> Path::getClippedLine (Line<float> line, const bool keepSectionOutsidePath) const
 {
     Line<float> result (line);
     const bool startInside = contains (line.getStart());
@@ -1103,10 +1106,10 @@ Line<float> Path::getClippedLine (const Line<float>& line, const bool keepSectio
     return result;
 }
 
-float Path::getLength (const AffineTransform& transform) const
+float Path::getLength (const AffineTransform& transform, float tolerance) const
 {
     float length = 0;
-    PathFlatteningIterator i (*this, transform);
+    PathFlatteningIterator i (*this, transform, tolerance);
 
     while (i.next())
         length += Line<float> (i.x1, i.y1, i.x2, i.y2).getLength();
@@ -1114,9 +1117,11 @@ float Path::getLength (const AffineTransform& transform) const
     return length;
 }
 
-Point<float> Path::getPointAlongPath (float distanceFromStart, const AffineTransform& transform) const
+Point<float> Path::getPointAlongPath (float distanceFromStart,
+                                      const AffineTransform& transform,
+                                      float tolerance) const
 {
-    PathFlatteningIterator i (*this, transform);
+    PathFlatteningIterator i (*this, transform, tolerance);
 
     while (i.next())
     {
@@ -1133,9 +1138,10 @@ Point<float> Path::getPointAlongPath (float distanceFromStart, const AffineTrans
 }
 
 float Path::getNearestPoint (const Point<float> targetPoint, Point<float>& pointOnPath,
-                             const AffineTransform& transform) const
+                             const AffineTransform& transform,
+                             float tolerance) const
 {
-    PathFlatteningIterator i (*this, transform);
+    PathFlatteningIterator i (*this, transform, tolerance);
     float bestPosition = 0, bestDistance = std::numeric_limits<float>::max();
     float length = 0;
     Point<float> pointOnLine;
diff --git a/modules/juce_graphics/geometry/juce_Path.h b/modules/juce_graphics/geometry/juce_Path.h
index 9a0bfe7063..6ddca5dd18 100644
--- a/modules/juce_graphics/geometry/juce_Path.h
+++ b/modules/juce_graphics/geometry/juce_Path.h
@@ -83,12 +83,14 @@ public:
     bool operator== (const Path&) const noexcept;
     bool operator!= (const Path&) const noexcept;
 
+    static const float defaultToleranceForTesting;
+    static const float defaultToleranceForMeasurement;
+
     //==============================================================================
     /** Returns true if the path doesn't contain any lines or curves. */
     bool isEmpty() const noexcept;
 
-    /** Returns the smallest rectangle that contains all points within the path.
-    */
+    /** Returns the smallest rectangle that contains all points within the path. */
     Rectangle<float> getBounds() const noexcept;
 
     /** Returns the smallest rectangle that contains all points within the path
@@ -110,7 +112,7 @@ public:
         @see closeSubPath, setUsingNonZeroWinding
     */
     bool contains (float x, float y,
-                   float tolerance = 1.0f) const;
+                   float tolerance = defaultToleranceForTesting) const;
 
     /** Checks whether a point lies within the path.
 
@@ -126,7 +128,7 @@ public:
         @see closeSubPath, setUsingNonZeroWinding
     */
     bool contains (const Point<float> point,
-                   float tolerance = 1.0f) const;
+                   float tolerance = defaultToleranceForTesting) const;
 
     /** Checks whether a line crosses the path.
 
@@ -138,8 +140,8 @@ public:
         so this method could return a false positive when your point is up to this distance
         outside the path's boundary.
     */
-    bool intersectsLine (const Line<float>& line,
-                         float tolerance = 1.0f);
+    bool intersectsLine (Line<float> line,
+                         float tolerance = defaultToleranceForTesting);
 
     /** Cuts off parts of a line to keep the parts that are either inside or
         outside this path.
@@ -153,12 +155,13 @@ public:
                                         that will be kept; if false its the section inside
                                         the path
     */
-    Line<float> getClippedLine (const Line<float>& line, bool keepSectionOutsidePath) const;
+    Line<float> getClippedLine (Line<float> line, bool keepSectionOutsidePath) const;
 
     /** Returns the length of the path.
         @see getPointAlongPath
     */
-    float getLength (const AffineTransform& transform = AffineTransform()) const;
+    float getLength (const AffineTransform& transform = AffineTransform(),
+                     float tolerance = defaultToleranceForMeasurement) const;
 
     /** Returns a point that is the specified distance along the path.
         If the distance is greater than the total length of the path, this will return the
@@ -166,15 +169,17 @@ public:
         @see getLength
     */
     Point<float> getPointAlongPath (float distanceFromStart,
-                                    const AffineTransform& transform = AffineTransform()) const;
+                                    const AffineTransform& transform = AffineTransform(),
+                                    float tolerance = defaultToleranceForMeasurement) const;
 
     /** Finds the point along the path which is nearest to a given position.
         This sets pointOnPath to the nearest point, and returns the distance of this point from the start
         of the path.
     */
-    float getNearestPoint (const Point<float> targetPoint,
+    float getNearestPoint (Point<float> targetPoint,
                            Point<float>& pointOnPath,
-                           const AffineTransform& transform = AffineTransform()) const;
+                           const AffineTransform& transform = AffineTransform(),
+                           float tolerance = defaultToleranceForMeasurement) const;
 
     //==============================================================================
     /** Removes all lines and curves, resetting the path completely. */
diff --git a/modules/juce_graphics/geometry/juce_PathIterator.cpp b/modules/juce_graphics/geometry/juce_PathIterator.cpp
index ce3c463101..76663ace05 100644
--- a/modules/juce_graphics/geometry/juce_PathIterator.cpp
+++ b/modules/juce_graphics/geometry/juce_PathIterator.cpp
@@ -26,8 +26,6 @@
  #pragma optimize ("t", on)
 #endif
 
-const float PathFlatteningIterator::defaultTolerance = 0.6f;
-
 //==============================================================================
 PathFlatteningIterator::PathFlatteningIterator (const Path& path_,
                                                 const AffineTransform& transform_,
diff --git a/modules/juce_graphics/geometry/juce_PathIterator.h b/modules/juce_graphics/geometry/juce_PathIterator.h
index 6994e28c32..0e0c5de795 100644
--- a/modules/juce_graphics/geometry/juce_PathIterator.h
+++ b/modules/juce_graphics/geometry/juce_PathIterator.h
@@ -53,7 +53,7 @@ public:
     */
     PathFlatteningIterator (const Path& path,
                             const AffineTransform& transform = AffineTransform(),
-                            float tolerance = defaultTolerance);
+                            float tolerance = Path::defaultToleranceForMeasurement);
 
     /** Destructor. */
     ~PathFlatteningIterator();
@@ -90,9 +90,6 @@ public:
     /** Returns true if the current segment is the last in the current sub-path. */
     bool isLastInSubpath() const noexcept;
 
-    /** This is the default value that should be used for the tolerance value (see the constructor parameters). */
-    static const float defaultTolerance;
-
 private:
     //==============================================================================
     const Path& path;
diff --git a/modules/juce_graphics/geometry/juce_PathStrokeType.cpp b/modules/juce_graphics/geometry/juce_PathStrokeType.cpp
index 7f917f629b..c0dd878983 100644
--- a/modules/juce_graphics/geometry/juce_PathStrokeType.cpp
+++ b/modules/juce_graphics/geometry/juce_PathStrokeType.cpp
@@ -570,7 +570,7 @@ namespace PathStrokeHelpers
 
         // Iterate the path, creating a list of the
         // left/right-hand lines along either side of it...
-        PathFlatteningIterator it (*sourcePath, transform, PathFlatteningIterator::defaultTolerance / extraAccuracy);
+        PathFlatteningIterator it (*sourcePath, transform, Path::defaultToleranceForMeasurement / extraAccuracy);
 
         Array <LineSection> subPath;
         subPath.ensureStorageAllocated (512);
@@ -668,7 +668,7 @@ void PathStrokeType::createDashedStroke (Path& destPath,
         return;
 
     Path newDestPath;
-    PathFlatteningIterator it (sourcePath, transform, PathFlatteningIterator::defaultTolerance / extraAccuracy);
+    PathFlatteningIterator it (sourcePath, transform, Path::defaultToleranceForMeasurement / extraAccuracy);
 
     bool first = true;
     int dashNum = 0;