diff --git a/src/path/Curve.js b/src/path/Curve.js
index 10926814..dae00bb7 100644
--- a/src/path/Curve.js
+++ b/src/path/Curve.js
@@ -1049,7 +1049,7 @@ new function() { // Scope for methods that require numerical integration
                 // Get length of total range
                 rangeLength = Numerical.integrate(ds, a, b,
                         getIterations(a, b));
-            if (abs(offset - rangeLength) <= tolerance) {
+            if (abs(offset - rangeLength) < tolerance) {
                 // Matched the end:
                 return forward ? b : a;
             } else if (abs(offset) > rangeLength) {
@@ -1115,7 +1115,7 @@ new function() { // Scope for methods that require numerical integration
             dp2 = getSignedDistance(q0x, q0y, q3x, q3y, v1[4], v1[5]),
             dp3 = getSignedDistance(q0x, q0y, q3x, q3y, v1[6], v1[7]),
             tMinNew, tMaxNew, tDiff;
-        if (q0x === q3x && uMax - uMin <= tolerance && recursion > 3) {
+        if (q0x === q3x && uMax - uMin < tolerance && recursion > 3) {
             // The fatline of Q has converged to a point, the clipping is not
             // reliable. Return the value we have even though we will miss the
             // precision.
diff --git a/src/path/PathItem.Boolean.js b/src/path/PathItem.Boolean.js
index 710f8c65..6608a956 100644
--- a/src/path/PathItem.Boolean.js
+++ b/src/path/PathItem.Boolean.js
@@ -138,15 +138,15 @@ PathItem.inject(new function() {
                     if (length <= curveLength) {
                         // If the selected location on the curve falls onto its
                         // beginning or end, use the curve's center instead.
-                        if (length <= tolerance
-                                || curveLength - length <= tolerance)
+                        if (length < tolerance
+                                || curveLength - length < tolerance)
                             length = curveLength / 2;
                         var curve = node.segment.getCurve(),
                             pt = curve.getPointAt(length),
                             // Determine if the curve is a horizontal linear
                             // curve by checking the slope of it's tangent.
                             hor = curve.isLinear() && Math.abs(curve
-                                    .getTangentAt(0.5, true).y) <= tolerance,
+                                    .getTangentAt(0.5, true).y) < tolerance,
                             path = curve._path;
                         if (path._parent instanceof CompoundPath)
                             path = path._parent;
@@ -320,7 +320,7 @@ PathItem.inject(new function() {
                             // Detect and exclude intercepts at 'end' of loops:
                             && (i === l - 1 || curve.next !== curves[i + 1])
                             && abs(Curve.evaluate(curve.next.values, 0, 0).x -x)
-                                <= tolerance
+                                < tolerance
                         // Detect 2nd case of a consecutive intercept, but make
                         // sure we're still on the same loop
                         || i > 0 && curve.previous === curves[i - 1]