diff --git a/demo/python/demo_custom_element.py b/demo/python/demo_custom_element.py
index ccd338099..0570cc82c 100644
--- a/demo/python/demo_custom_element.py
+++ b/demo/python/demo_custom_element.py
@@ -9,7 +9,7 @@
 
 import basix
 import numpy as np
-from basix import CellType, MapType, PolynomialType, LatticeType, SobolevSpace, PolysetType
+from basix import CellType, MapType, PolynomialType, LatticeType, SobolevSpace
 
 # Lagrange element with bubble
 # ============================
@@ -67,7 +67,7 @@
 # We compute these integrals using a degree 4 quadrature rule (this is the largest degree
 # that the integrand will be, so these integrals will be exact).
 
-pts, wts = basix.make_quadrature(CellType.quadrilateral, PolysetType.standard, 4)
+pts, wts = basix.quadrature.make_quadrature(CellType.quadrilateral, 4)
 poly = basix.tabulate_polynomials(PolynomialType.legendre, CellType.quadrilateral, 2, pts)
 x = pts[:, 0]
 y = pts[:, 1]
@@ -188,7 +188,7 @@
 wcoeffs[0, 0] = 1
 wcoeffs[1, 3] = 1
 
-pts, wts = basix.make_quadrature(CellType.triangle, PolysetType.standard, 2)
+pts, wts = basix.quadrature.make_quadrature(CellType.triangle, 2)
 poly = basix.tabulate_polynomials(PolynomialType.legendre, CellType.triangle, 1, pts)
 x = pts[:, 0]
 y = pts[:, 1]
@@ -203,7 +203,7 @@
 # the element are integrals. We begin by defining a degree 1 quadrature rule on an interval.
 # This quadrature rule will be used to integrate on the edges of the triangle.
 
-pts, wts = basix.make_quadrature(CellType.interval, PolysetType.standard, 1)
+pts, wts = basix.quadrature.make_quadrature(CellType.interval, 1)
 
 # The points associated with each edge are calculated by mapping the quadrature points to each edge.
 
diff --git a/demo/python/demo_custom_element_conforming_cr.py b/demo/python/demo_custom_element_conforming_cr.py
index a367815c4..ba6b2ff29 100644
--- a/demo/python/demo_custom_element_conforming_cr.py
+++ b/demo/python/demo_custom_element_conforming_cr.py
@@ -62,7 +62,7 @@ def create_ccr_triangle(degree):
         wcoeffs[dof_n, dof_n] = 1
         dof_n += 1
 
-    pts, wts = basix.make_quadrature(CellType.triangle, PolysetType.standard, 2 * (degree + 1))
+    pts, wts = basix.quadrature.make_quadrature(CellType.triangle, 2 * (degree + 1))
     poly = basix.tabulate_polynomials(PolynomialType.legendre, CellType.triangle, degree + 1, pts)
     for i in range(1, degree):
         x = pts[:, 0]
diff --git a/demo/python/demo_facet_integral.py b/demo/python/demo_facet_integral.py
index 5f5bee215..70a279f09 100644
--- a/demo/python/demo_facet_integral.py
+++ b/demo/python/demo_facet_integral.py
@@ -15,7 +15,7 @@
 
 import basix
 import numpy as np
-from basix import ElementFamily, CellType, LagrangeVariant, PolysetType
+from basix import ElementFamily, CellType, LagrangeVariant
 
 # We define a degree 3 Lagrange space on a tetrahedron.
 
@@ -26,7 +26,7 @@
 # rule on a triangle. We use an order 3 rule so that we can integrate the
 # basis functions in our space exactly.
 
-points, weights = basix.make_quadrature(CellType.triangle, PolysetType.standard, 3)
+points, weights = basix.quadrature.make_quadrature(CellType.triangle, 3)
 
 # Next, we must map the quadrature points to our facet. We use the function
 # `geometry` to get the coordinates of the vertices of the tetrahedron, and
diff --git a/demo/python/demo_quadrature.py b/demo/python/demo_quadrature.py
index a645e54f5..1ccc50cb3 100644
--- a/demo/python/demo_quadrature.py
+++ b/demo/python/demo_quadrature.py
@@ -28,14 +28,14 @@
 # `make_quadrature` returns two values: the points and the weights of the
 # quadrature rule.
 
-points, weights = basix.make_quadrature(CellType.triangle, PolysetType.standard, 4)
+points, weights = basix.quadrature.make_quadrature(CellType.triangle, 4)
 
 # If we want to control the type of quadrature used, we can pass in three
 # inputs to `make_quadrautre`. For example, the following code would force basix
 # to use a Gauss-Jacobi quadrature rule:
 
-points, weights = basix.make_quadrature(
-    basix.QuadratureType.gauss_jacobi, CellType.triangle, PolysetType.standard, 4)
+points, weights = basix.quadrature.make_quadrature(
+    CellType.triangle, 4, rule=basix.QuadratureType.gauss_jacobi)
 
 # We now use this quadrature rule to integrate the functions :math:`f(x,y)=x^3y`
 # and :math:`g(x,y)=x^3y^2` over the triangle. The exact values of these integrals