diff --git a/src/path/Curve.js b/src/path/Curve.js
index ae895b66..ec018b2b 100644
--- a/src/path/Curve.js
+++ b/src/path/Curve.js
@@ -1076,7 +1076,12 @@ new function() { // Scope for methods that require numerical integration
             tMin, tMax, uMin, uMax, oldTDiff, reverse, recursion) {
 /*#*/ if (__options.fatlineClipping) {
         // Avoid deeper recursion.
-        if (recursion > 20)
+        // NOTE: @iconexperience determined that more than 20 recursions are
+        // needed sometimes, depending on the tDiff threshold values further
+        // below when determining which curve converges the least. He also
+        // recommended a threshold of 0.5 instead of the initial 0.8
+        // See: https://github.com/paperjs/paper.js/issues/565
+        if (recursion > 32)
             return;
         // Let P be the first curve and Q be the second
         var q0x = v2[0], q0y = v2[1], q3x = v2[6], q3y = v2[7],
@@ -1127,7 +1132,7 @@ new function() { // Scope for methods that require numerical integration
             tMaxNew = tMax * tMaxClip + tMin * (1 - tMaxClip);
         }
         // Check if we need to subdivide the curves
-        if (oldTDiff > 0.8 && tDiff > 0.8) {
+        if (oldTDiff > 0.5 && tDiff > 0.5) {
             // Subdivide the curve which has converged the least.
             if (tMaxNew - tMinNew > uMax - uMin) {
                 var parts = Curve.subdivide(v1, 0.5),