diff --git a/Lib/fontTools/misc/bezierTools.py b/Lib/fontTools/misc/bezierTools.py
index 21ab0a5d0..a1a707b09 100644
--- a/Lib/fontTools/misc/bezierTools.py
+++ b/Lib/fontTools/misc/bezierTools.py
@@ -1370,6 +1370,11 @@ def _curve_curve_intersections_t(
     return unique_values
 
 
+def _is_linelike(segment):
+    maybeline = _alignment_transformation(segment).transformPoints(segment)
+    return all(math.isclose(p[1], 0.0) for p in maybeline)
+
+
 def curveCurveIntersections(curve1, curve2):
     """Finds intersections between a curve and a curve.
 
@@ -1391,6 +1396,17 @@ def curveCurveIntersections(curve1, curve2):
         >>> intersections[0].pt
         (81.7831487395506, 109.88904552375288)
     """
+    if _is_linelike(curve1):
+        line1 = curve1[0], curve1[-1]
+        if _is_linelike(curve2):
+            line2 = curve2[0], curve2[-1]
+            return lineLineIntersections(*line1, *line2)
+        else:
+            return curveLineIntersections(curve2, line1)
+    elif _is_linelike(curve2):
+        line2 = curve2[0], curve2[-1]
+        return curveLineIntersections(curve1, line2)
+
     intersection_ts = _curve_curve_intersections_t(curve1, curve2)
     return [
         Intersection(pt=segmentPointAtT(curve1, ts[0]), t1=ts[0], t2=ts[1])
diff --git a/Tests/misc/bezierTools_test.py b/Tests/misc/bezierTools_test.py
index 8a3e2ecda..ce8a9e17e 100644
--- a/Tests/misc/bezierTools_test.py
+++ b/Tests/misc/bezierTools_test.py
@@ -4,6 +4,7 @@ from fontTools.misc.bezierTools import (
     calcQuadraticArcLength,
     calcCubicBounds,
     curveLineIntersections,
+    curveCurveIntersections,
     segmentPointAtT,
     splitLine,
     splitQuadratic,
@@ -189,3 +190,10 @@ def test_calcQuadraticArcLength():
     assert calcQuadraticArcLength(
         (210, 333), (289, 333), (326.5, 290.5)
     ) == pytest.approx(127.9225)
+
+
+def test_intersections_linelike():
+    seg1 = [(0.0, 0.0), (0.0, 0.25), (0.0, 0.75), (0.0, 1.0)]
+    seg2 = [(0.0, 0.5), (0.25, 0.5), (0.75, 0.5), (1.0, 0.5)]
+    pt = curveCurveIntersections(seg1, seg2)[0][0]
+    assert pt == (0.0, 0.5)