diff -dur orig_polygon/detail/minkowski.hpp polygon/detail/minkowski.hpp
--- orig_polygon/detail/minkowski.hpp	2011-10-27 15:35:55.318381000 -0400
+++ polygon/detail/minkowski.hpp	2011-10-27 15:11:15.283021900 -0400
@@ -82,17 +82,18 @@
 }
   template<typename T>
   inline polygon_set_data<T>&
-  polygon_set_data<T>::resize(coordinate_type resizing, bool corner_fill_arc, unsigned int num_circle_segments) {
+  polygon_set_data<T>::resize(coordinate_type resizing, bool corner_fill_arc, unsigned int num_circle_segments,
+                              double minUnroundedAngleDegrees) {
     using namespace ::boost::polygon::operators;
+    if(resizing == 0) return *this;
+    if(empty()) return *this;
     if(!corner_fill_arc) {
       if(resizing < 0)
         return shrink(-resizing);
-      if(resizing > 0)
+      else
         return bloat(resizing);
-      return *this;
     }
-    if(resizing == 0) return *this;
-    if(empty()) return *this;
+
     if(num_circle_segments < 3) num_circle_segments = 4;
     rectangle_data<coordinate_type> rect;
     extents(rect);
@@ -100,13 +101,28 @@
       ::boost::polygon::bloat(rect, 10);
       (*this) = rect - (*this); //invert
     }
-    //make_arc(std::vector<point_data< T> >& return_points,  
-    //point_data< double> start, point_data< double>  end,
-    //point_data< double> center,  double r, unsigned int num_circle_segments)      
+
+    // scale arc up so that minimum radius corresponds to 'resizing',
+    // for bug ticket #6063.
+    const double our_pi=3.1415926535897932384626433832795028841971;
+    double arcRadScaling = 1.0/cos(2.0*our_pi/double(num_circle_segments)/2.0);
+    double arcRadius = double(std::abs(resizing))*arcRadScaling;
+
+    if(minUnroundedAngleDegrees < 180.0)
+    {
+        // Don't round corners less than given angle (in radians).
+        // We do this by setting the minimum radius of the 'circle' to correspond to
+        // the distance to the 'elbow' created by normal offset of a corner with the given angle.
+        // e.g. an 90-degree corner with an offset of 1 will generate an elbow at distance sqrt(2).
+        // This will of course offset non-corners more than the given resizing, but the extra area
+        // gets chopped off by the intersection with normal_offset_result, below.
+        double elbowDist = double(std::abs(resizing))/sin(minUnroundedAngleDegrees*our_pi/180.0/2.0);
+        arcRadius = elbowDist*arcRadScaling;
+    }
+
     std::vector<point_data<coordinate_type> > circle;
-    point_data<double> center(0.0, 0.0), start(0.0, (double)resizing);
-    make_arc(circle, start, start, center, std::abs((double)resizing),
-             num_circle_segments);
+    point_data<double> center(0.0, 0.0), start(0.0, arcRadius);
+    make_arc(circle, start, start, center, arcRadius, num_circle_segments);
     polygon_data<coordinate_type> poly;
     set_points(poly, circle.begin(), circle.end());
     polygon_set_data<coordinate_type> offset_set;
@@ -114,10 +130,19 @@
     polygon_set_data<coordinate_type> result;
     detail::minkowski_offset<coordinate_type>::convolve_two_polygon_sets
       (result, *this, offset_set);
+
+    // Intersect with result of 'normal' (non-minkowski-sum) offset,
+    // to remove offsets larger than the given 'resizing' when not near corners.
+    // Also for bug ticket #6063
+    polygon_set_data<coordinate_type> normal_offset_result(*this);
+    normal_offset_result.bloat(std::abs(resizing));
+    result = result & normal_offset_result;
+
     if(resizing < 0) {
       result = result & rect;//eliminate overhang
       result = result ^ rect;//invert
     }
+
     *this = result;
     return *this;
   }
diff -dur orig_polygon/polygon_set_data.hpp polygon/polygon_set_data.hpp
--- orig_polygon/polygon_set_data.hpp	2011-10-27 15:35:55.347381000 -0400
+++ polygon/polygon_set_data.hpp	2011-10-27 15:38:27.231381000 -0400
@@ -359,7 +359,8 @@
     }
 
     inline polygon_set_data&
-    resize(coordinate_type resizing, bool corner_fill_arc = false, unsigned int num_circle_segments=0);
+    resize(coordinate_type resizing, bool corner_fill_arc = false, unsigned int num_circle_segments=0,
+           double minUnroundedAngleDegrees=180.0);
 
     template <typename transform_type>
     inline polygon_set_data&