diff --git a/Lib/fontTools/pens/qu2cuPen.py b/Lib/fontTools/pens/qu2cuPen.py
index a04d1f61e..55dfeeff6 100644
--- a/Lib/fontTools/pens/qu2cuPen.py
+++ b/Lib/fontTools/pens/qu2cuPen.py
@@ -13,7 +13,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-from fontTools.qu2cu import quadratics_to_curves
+from fontTools.qu2cu import quadratic_to_curves
 from fontTools.pens.filterPen import ContourFilterPen
 from fontTools.pens.reverseContourPen import ReverseContourPen
 
@@ -48,7 +48,7 @@ class Qu2CuPen(ContourFilterPen):
         self.stats = stats
 
     def _quadratics_to_curve(self, q):
-        curves = quadratics_to_curves(q, self.max_err, self.all_cubic)
+        curves = quadratic_to_curves(q, self.max_err, self.all_cubic)
         if self.stats is not None:
             n = str(len(curves))
             self.stats[n] = self.stats.get(n, 0) + 1
diff --git a/Lib/fontTools/qu2cu/benchmark.py b/Lib/fontTools/qu2cu/benchmark.py
index f6edc8679..0839ab439 100644
--- a/Lib/fontTools/qu2cu/benchmark.py
+++ b/Lib/fontTools/qu2cu/benchmark.py
@@ -18,7 +18,7 @@ def generate_curve():
 def setup_quadratic_to_curves():
     curve = generate_curve()
     quadratics = curve_to_quadratic(curve, MAX_ERR)
-    return quadratics, MAX_ERR
+    return [quadratics], MAX_ERR
 
 
 def run_benchmark(module, function, setup_suffix="", repeat=10, number=20):
diff --git a/Lib/fontTools/qu2cu/qu2cu.py b/Lib/fontTools/qu2cu/qu2cu.py
index 414dce584..69ebb1281 100644
--- a/Lib/fontTools/qu2cu/qu2cu.py
+++ b/Lib/fontTools/qu2cu/qu2cu.py
@@ -26,7 +26,7 @@ from fontTools.misc.bezierTools import splitCubicAtTC
 from collections import namedtuple
 
 
-__all__ = ["quadratic_to_curves", "quadratics_to_curves"]
+__all__ = ["quadratic_to_curves"]
 
 
 if cython.compiled:
@@ -164,7 +164,7 @@ def add_implicit_on_curves(p):
     return q
 
 
-def quadratics_to_curves(pp, tolerance=0.5, all_cubic=False):
+def quadratic_to_curves(pp, tolerance=0.5, all_cubic=False):
     """Convers a connecting list of quadratic splines to a list of quadratic
     and cubic curves.
 
@@ -207,41 +207,6 @@ def quadratics_to_curves(pp, tolerance=0.5, all_cubic=False):
     return curves
 
 
-def quadratic_to_curves(q, tolerance=0.5, all_cubic=False):
-    """Convers a quadratic spline to a list of quadratic and cubic curves.
-
-    The quadratic spline is specified as a list of points, each of which is
-    a 2-tuple of X,Y coordinates. The first and last points are on-curve points
-    and the rest are off-curve points, with an implied on-curve point in the
-    middle between every two consequtive off-curve points.
-
-    The output is a list of tuples. Each tuple is either of length three, for
-    a quadratic curve, or four, for a cubic curve.  Each curve's last point
-    is the same as the next curve's first point.
-
-    q: quadratic spline
-    tolerance: absolute error tolerance; defaults to 0.5
-    all_cubic: if True, only cubic curves are generated; defaults to False
-    """
-    is_complex = type(q[0]) is complex
-    if not is_complex:
-        q = [complex(x, y) for (x, y) in q]
-
-    costs = [0]
-    for i in range(len(q) - 2):
-        costs.append(i + 1)
-        costs.append(i + 2)
-    costs.append(len(q) - 1)
-    costs.append(len(q))
-    q = add_implicit_on_curves(q)
-
-    curves = spline_to_curves(q, costs, tolerance, all_cubic)
-
-    if not is_complex:
-        curves = [tuple((c.real, c.imag) for c in curve) for curve in curves]
-    return curves
-
-
 Solution = namedtuple("Solution", ["num_points", "error", "start_index", "is_cubic"])
 
 
@@ -361,7 +326,7 @@ def main():
         "cu2qu tolerance %g. qu2cu tolerance %g." % (tolerance, reconstruct_tolerance)
     )
     print("One random cubic turned into %d quadratics." % len(quadratics))
-    curves = quadratic_to_curves(quadratics, reconstruct_tolerance)
+    curves = quadratic_to_curves([quadratics], reconstruct_tolerance)
     print("Those quadratics turned back into %d cubics. " % len(curves))
     print("Original curve:", curve)
     print("Reconstructed curve(s):", curves)
diff --git a/Tests/qu2cu/qu2cu_test.py b/Tests/qu2cu/qu2cu_test.py
index bb45435f1..fae240cc9 100644
--- a/Tests/qu2cu/qu2cu_test.py
+++ b/Tests/qu2cu/qu2cu_test.py
@@ -15,7 +15,7 @@
 import unittest
 import pytest
 
-from fontTools.qu2cu import quadratic_to_curves, quadratics_to_curves
+from fontTools.qu2cu import quadratic_to_curves
 from fontTools.qu2cu.qu2cu import main as qu2cu_main
 from fontTools.qu2cu.benchmark import main as benchmark_main
 
@@ -81,11 +81,7 @@ class Qu2CuTest:
             for curve in expected
         ]
 
-        if len(quadratics) == 1:
-            c = quadratic_to_curves(quadratics[0], tolerance, cubic_only)
-            assert c == expected
-
-        c = quadratics_to_curves(quadratics, tolerance, cubic_only)
+        c = quadratic_to_curves(quadratics, tolerance, cubic_only)
         assert c == expected
 
     def test_roundtrip(self):
@@ -97,7 +93,7 @@ class Qu2CuTest:
         tolerance = 1
 
         splines = [curve_to_quadratic(c, tolerance) for c in curves]
-        reconsts = [quadratic_to_curves(spline, tolerance) for spline in splines]
+        reconsts = [quadratic_to_curves([spline], tolerance) for spline in splines]
 
         for curve, reconst in zip(curves, reconsts):
             assert len(reconst) == 1