diff --git a/svgpathtools/path.py b/svgpathtools/path.py
index 7418615..5903efe 100644
--- a/svgpathtools/path.py
+++ b/svgpathtools/path.py
@@ -711,6 +711,19 @@ class Line(object):
         Note: This will fail if the two segments coincide for more than a
         finite collection of points.
         tol is not used."""
+        if isinstance(other_seg, (Line, QuadraticBezier, CubicBezier)):
+            ob = [e.real for e in other_seg.bpoints()]
+            sb = [e.real for e in self.bpoints()]
+            if min(ob) > max(sb):
+                return []
+            if max(ob) < min(sb):
+                return []
+            ob = [e.imag for e in other_seg.bpoints()]
+            sb = [e.imag for e in self.bpoints()]
+            if min(ob) > max(sb):
+                return []
+            if max(ob) < min(sb):
+                return []
         if isinstance(other_seg, Line):
             assert other_seg.end != other_seg.start and self.end != self.start
             assert self != other_seg
@@ -1038,6 +1051,19 @@ class QuadraticBezier(object):
         self.point(t1) == other_seg.point(t2).
         Note: This will fail if the two segments coincide for more than a
         finite collection of points."""
+        if isinstance(other_seg, (Line, QuadraticBezier, CubicBezier)):
+            ob = [e.real for e in other_seg.bpoints()]
+            sb = [e.real for e in self.bpoints()]
+            if min(ob) > max(sb):
+                return []
+            if max(ob) < min(sb):
+                return []
+            ob = [e.imag for e in other_seg.bpoints()]
+            sb = [e.imag for e in self.bpoints()]
+            if min(ob) > max(sb):
+                return []
+            if max(ob) < min(sb):
+                return []
         if isinstance(other_seg, Line):
             return bezier_by_line_intersections(self, other_seg)
         elif isinstance(other_seg, QuadraticBezier):
@@ -1298,6 +1324,19 @@ class CubicBezier(object):
             This will fail if the two segments coincide for more than a
             finite collection of points.
         """
+        if isinstance(other_seg, (Line, QuadraticBezier, CubicBezier)):
+            ob = [e.real for e in other_seg.bpoints()]
+            sb = [e.real for e in self.bpoints()]
+            if min(ob) > max(sb):
+                return []
+            if max(ob) < min(sb):
+                return []
+            ob = [e.imag for e in other_seg.bpoints()]
+            sb = [e.imag for e in self.bpoints()]
+            if min(ob) > max(sb):
+                return []
+            if max(ob) < min(sb):
+                return []
         if isinstance(other_seg, Line):
             return bezier_by_line_intersections(self, other_seg)
         elif (isinstance(other_seg, QuadraticBezier) or
diff --git a/test/test_path.py b/test/test_path.py
index 6a19d10..4190f70 100644
--- a/test/test_path.py
+++ b/test/test_path.py
@@ -1,6 +1,7 @@
 # External dependencies
 from __future__ import division, absolute_import, print_function
 import os
+import time
 from sys import version_info
 import unittest
 from math import sqrt, pi
@@ -1495,6 +1496,50 @@ class Test_intersect(unittest.TestCase):
             self.assertTrue(len(yix) == 1)
         ###################################################################
 
+    def test_random_intersections(self):
+        from random import Random
+        r = Random()
+        distance = 100
+        distribution = 10000
+        count = 500
+
+        def random_complex(offset_x=0.0, offset_y=0.0):
+            return complex(r.random() * distance + offset_x, r.random() * distance + offset_y)
+
+        def random_line():
+            offset_x = r.random() * distribution
+            offset_y = r.random() * distribution
+            return Line(random_complex(offset_x, offset_y), random_complex(offset_x, offset_y))
+
+        def random_quad():
+            offset_x = r.random() * distribution
+            offset_y = r.random() * distribution
+            return QuadraticBezier(random_complex(offset_x, offset_y), random_complex(offset_x, offset_y), random_complex(offset_x, offset_y))
+
+        def random_cubic():
+            offset_x = r.random() * distribution
+            offset_y = r.random() * distribution
+            return CubicBezier(random_complex(offset_x, offset_y), random_complex(offset_x, offset_y), random_complex(offset_x, offset_y), random_complex(offset_x, offset_y))
+
+        def random_path():
+            path = Path()
+            for i in range(count):
+                type_segment = random.randint(0, 3)
+                if type_segment == 0:
+                    path.append(random_line())
+                if type_segment == 1:
+                    path.append(random_quad())
+                if type_segment == 2:
+                    path.append(random_cubic())
+            return path
+
+        path1 = random_path()
+        path2 = random_path()
+        t = time.time()
+        intersections = path1.intersect(path2)
+        print("\nFound {} intersections in {} seconds.\n"
+              "".format(len(intersections), time.time() - t))
+
     def test_line_line_0(self):
         l0 = Line(start=(25.389999999999997+99.989999999999995j),
                   end=(25.389999999999997+90.484999999999999j))