diff --git a/ChangeLog b/ChangeLog
index dd9f48cfe..1efd28a21 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,21 @@
+2019-04-29  Alexei Podtelezhnikov  <apodtele@gmail.com>
+
+	[smooth] Simplify cubic Bézier flattening.
+
+	The previous implementation is correct but it is too complex.
+	The revised algorithm is based on the fact that each split moves
+	the control points closer to the trisection points on the chord.
+	The corresponding distances are good surrogates for the curve
+	deviation from the straight line.
+
+	This cubic flattening algorithm is somewhat similar to the conic
+	algorithm based the distance from the control point to the middle of
+	the chord.  The cubic distances, however, decrease less predictably
+	but are easy enough to calculate on each step.
+
+	* src/smooth/ftgrays.c (gray_render_cubic): Replace the split
+	condition.
+
 2019-04-26  Alexei Podtelezhnikov  <apodtele@gmail.com>
 
 	[smooth] Bithacks and cosmetics.
diff --git a/src/smooth/ftgrays.c b/src/smooth/ftgrays.c
index b421fc8f4..72ab546a5 100644
--- a/src/smooth/ftgrays.c
+++ b/src/smooth/ftgrays.c
@@ -1093,9 +1093,6 @@ typedef ptrdiff_t  FT_PtrDist;
   {
     FT_Vector   bez_stack[16 * 3 + 1];  /* enough to accommodate bisections */
     FT_Vector*  arc = bez_stack;
-    TPos        dx, dy, dx_, dy_;
-    TPos        dx1, dy1, dx2, dy2;
-    TPos        L, s, s_limit;
 
 
     arc[0].x = UPSCALE( to->x );
@@ -1124,45 +1121,13 @@ typedef ptrdiff_t  FT_PtrDist;
 
     for (;;)
     {
-      /* Decide whether to split or draw. See `Rapid Termination          */
-      /* Evaluation for Recursive Subdivision of Bezier Curves' by Thomas */
-      /* F. Hain, at                                                      */
-      /* http://www.cis.southalabama.edu/~hain/general/Publications/Bezier/Camera-ready%20CISST02%202.pdf */
-
-      /* dx and dy are x and y components of the P0-P3 chord vector. */
-      dx = dx_ = arc[3].x - arc[0].x;
-      dy = dy_ = arc[3].y - arc[0].y;
-
-      L = FT_HYPOT( dx_, dy_ );
-
-      /* Avoid possible arithmetic overflow below by splitting. */
-      if ( L > 32767 )
-        goto Split;
-
-      /* Max deviation may be as much as (s/L) * 3/4 (if Hain's v = 1). */
-      s_limit = L * (TPos)( ONE_PIXEL / 6 );
-
-      /* s is L * the perpendicular distance from P1 to the line P0-P3. */
-      dx1 = arc[1].x - arc[0].x;
-      dy1 = arc[1].y - arc[0].y;
-      s = FT_ABS( SUB_LONG( MUL_LONG( dy, dx1 ), MUL_LONG( dx, dy1 ) ) );
-
-      if ( s > s_limit )
-        goto Split;
-
-      /* s is L * the perpendicular distance from P2 to the line P0-P3. */
-      dx2 = arc[2].x - arc[0].x;
-      dy2 = arc[2].y - arc[0].y;
-      s = FT_ABS( SUB_LONG( MUL_LONG( dy, dx2 ), MUL_LONG( dx, dy2 ) ) );
-
-      if ( s > s_limit )
-        goto Split;
-
-      /* Split super curvy segments where the off points are so far
-         from the chord that the angles P0-P1-P3 or P0-P2-P3 become
-         acute as detected by appropriate dot products. */
-      if ( dx1 * ( dx1 - dx ) + dy1 * ( dy1 - dy ) > 0 ||
-           dx2 * ( dx2 - dx ) + dy2 * ( dy2 - dy ) > 0 )
+      /* with each split, control points quickly converge towards  */
+      /* chord trisection points and the vanishing distances below */
+      /* indicate when the segment is flat enough to draw          */
+      if ( FT_ABS( 2 * arc[0].x - 3 * arc[1].x + arc[3].x ) > ONE_PIXEL / 2 ||
+           FT_ABS( 2 * arc[0].y - 3 * arc[1].y + arc[3].y ) > ONE_PIXEL / 2 ||
+           FT_ABS( arc[0].x - 3 * arc[2].x + 2 * arc[3].x ) > ONE_PIXEL / 2 ||
+           FT_ABS( arc[0].y - 3 * arc[2].y + 2 * arc[3].y ) > ONE_PIXEL / 2 )
         goto Split;
 
       gray_render_line( RAS_VAR_ arc[0].x, arc[0].y );