diff --git a/src/plots/cartesian/axes.js b/src/plots/cartesian/axes.js
index 7ca242fb687..bd872d7f9af 100644
--- a/src/plots/cartesian/axes.js
+++ b/src/plots/cartesian/axes.js
@@ -804,13 +804,18 @@ axes.calcTicks = function calcTicks(ax) {
         endtick = (axrev) ? Math.max(-0.5, endtick) :
             Math.min(ax._categories.length - 0.5, endtick);
     }
+
+    var xPrevious = null;
+    var maxTicks = Math.max(1000, ax._length || 0);
     for(var x = ax._tmin;
             (axrev) ? (x >= endtick) : (x <= endtick);
             x = axes.tickIncrement(x, ax.dtick, axrev, ax.calendar)) {
-        vals.push(x);
+        // prevent infinite loops - no more than one tick per pixel,
+        // and make sure each value is different from the previous
+        if(vals.length > maxTicks || x === xPrevious) break;
+        xPrevious = x;
 
-        // prevent infinite loops
-        if(vals.length > 1000) break;
+        vals.push(x);
     }
 
     // save the last tick as well as first, so we can
diff --git a/test/jasmine/tests/axes_test.js b/test/jasmine/tests/axes_test.js
index a48525f952f..b76259e1e48 100644
--- a/test/jasmine/tests/axes_test.js
+++ b/test/jasmine/tests/axes_test.js
@@ -2225,6 +2225,38 @@ describe('Test axes', function() {
                 ['2000-01-01 11:00:00.0001', 'Jan 1, 2000, 11:00:00.0001']
             ]);
         });
+
+        it('avoids infinite loops due to rounding errors', function() {
+            var textOut = mockCalc({
+                type: 'linear',
+                tickmode: 'linear',
+                tick0: 1e200,
+                dtick: 1e-200,
+                range: [1e200, 2e200]
+            });
+
+            // This actually gives text '-Infinity' because it can't
+            // calculate the first tick properly, but since it's not going to
+            // be able to do any better with the rest, we don't much care.
+            expect(textOut.length).toBe(1);
+        });
+
+        it('truncates at the greater of 1001 ticks or one per pixel', function() {
+            var ax = {
+                type: 'linear',
+                tickmode: 'linear',
+                tick0: 0,
+                dtick: 1,
+                range: [0, 1e6],
+                _length: 100
+            };
+
+            expect(mockCalc(ax).length).toBe(1001);
+
+            ax._length = 10000;
+
+            expect(mockCalc(ax).length).toBe(10001);
+        });
     });
 
     describe('autoBin', function() {