diff --git a/src/cairo-arc.c b/src/cairo-arc.c
index 390397bae..f9249dbeb 100644
--- a/src/cairo-arc.c
+++ b/src/cairo-arc.c
@@ -99,7 +99,7 @@ _arc_max_angle_for_tolerance_normalized (double tolerance)
     do {
 	angle = M_PI / i++;
 	error = _arc_error_normalized (angle);
-    } while (error > tolerance);
+    } while (error > tolerance && error > __DBL_EPSILON__);
 
     return angle;
 }