diff --git a/src/curve/monotone.js b/src/curve/monotone.js
index f36b7ac..2599031 100644
--- a/src/curve/monotone.js
+++ b/src/curve/monotone.js
@@ -9,8 +9,8 @@ function sign(x) {
 function slope3(that, x2, y2) {
   var h0 = that._x1 - that._x0,
       h1 = x2 - that._x1,
-      s0 = (that._y1 - that._y0) / h0,
-      s1 = (y2 - that._y1) / h1,
+      s0 = (that._y1 - that._y0) / (h0 || h1 < 0 && -0),
+      s1 = (y2 - that._y1) / (h1 || h0 < 0 && -0),
       p = (s0 * h1 + s1 * h0) / (h0 + h1);
   return (sign(s0) + sign(s1)) * Math.min(Math.abs(s0), Math.abs(s1), 0.5 * Math.abs(p)) || 0;
 }
diff --git a/test/curve/monotoneX-test.js b/test/curve/monotoneX-test.js
index 30baaf1..c5efb26 100644
--- a/test/curve/monotoneX-test.js
+++ b/test/curve/monotoneX-test.js
@@ -27,6 +27,13 @@ tape("line.curve(curveMonotoneX)(data) handles duplicate x-values", function(tes
   test.end();
 });
 
+tape("line.curve(curveMonotoneX)(data) handles segments of infinite slope", function(test) {
+  var l = shape.line().curve(shape.curveMonotoneX);
+  test.pathEqual(l([[0, 200], [100, 150], [100, 50], [200, 0]]), "M0,200C33.333333,191.666667,66.666667,183.333333,100,150C100,150,100,50,100,50C133.333333,16.666667,166.666667,8.333333,200,0");
+  test.pathEqual(l([[200, 0], [100, 50], [100, 150], [0, 200]]), "M200,0C166.666667,8.333333,133.333333,16.666667,100,50C100,50,100,150,100,150C66.666667,183.333333,33.333333,191.666667,0,200");
+  test.end();
+});
+
 tape("line.curve(curveMonotoneX)(data) ignores coincident points", function(test) {
   var l = shape.line().curve(shape.curveMonotoneX),
       p = l([[0, 200], [50, 200], [100, 100], [150, 0], [200, 0]]);
diff --git a/test/curve/monotoneY-test.js b/test/curve/monotoneY-test.js
index f2eab0c..690252a 100644
--- a/test/curve/monotoneY-test.js
+++ b/test/curve/monotoneY-test.js
@@ -27,6 +27,13 @@ tape("line.curve(curveMonotoneY)(data) handles duplicate x-values", function(tes
   test.end();
 });
 
+tape("line.curve(curveMonotoneY)(data) handles segments of infinite slope", function(test) {
+  var l = shape.line().curve(shape.curveMonotoneY);
+  test.pathEqual(l([[0, 200], [100, 150], [100, 50], [200, 0]].map(reflect)), "M200,0C191.666667,33.333333,183.333333,66.666667,150,100C150,100,50,100,50,100C16.666667,133.333333,8.333333,166.666667,0,200");
+  test.pathEqual(l([[200, 0], [100, 50], [100, 150], [0, 200]].map(reflect)), "M0,200C8.333333,166.666667,16.666667,133.333333,50,100C50,100,150,100,150,100C183.333333,66.666667,191.666667,33.333333,200,0");
+  test.end();
+});
+
 tape("line.curve(curveMonotoneY)(data) ignores coincident points", function(test) {
   var l = shape.line().curve(shape.curveMonotoneY),
       p = l([[0, 200], [50, 200], [100, 100], [150, 0], [200, 0]].map(reflect));