diff --git a/src/xspline/core.py b/src/xspline/core.py
index aec9892..0f6b4e6 100644
--- a/src/xspline/core.py
+++ b/src/xspline/core.py
@@ -278,7 +278,7 @@ def __init__(self,
                  degree,
                  l_linear=False,
                  r_linear=False,
-                 include_first_basis: bool = False):
+                 include_first_basis: bool = True):
         r"""Constructor of the XSpline class.
 
         knots (numpy.ndarray):
@@ -301,7 +301,7 @@ def __init__(self,
         self.degree = degree
         self.l_linear = l_linear
         self.r_linear = r_linear
-        self.include_first_basis = include_first_basis
+        self.basis_start = int(not include_first_basis)
 
         # dimensions
         self.num_knots = knots.size
@@ -321,7 +321,7 @@ def __init__(self,
         self.inner_lb = self.inner_knots[0]
         self.inner_ub = self.inner_knots[-1]
 
-        self.num_spline_bases = self.inner_knots.size - 1 + self.degree - self.include_first_basis
+        self.num_spline_bases = self.inner_knots.size - 1 + self.degree - self.basis_start
 
     def domain(self, idx, l_extra=False, r_extra=False):
         """Return the support of the XSpline.
@@ -651,8 +651,7 @@ def design_mat(self, x, l_extra=False, r_extra=False):
         """
         mat = np.vstack([
             self.fun(x, idx, l_extra=l_extra, r_extra=r_extra)
-            for idx in range(self.include_first_basis,
-                             self.num_spline_bases)
+            for idx in range(self.basis_start, self.num_spline_bases)
         ]).T
         return mat
 
@@ -680,8 +679,7 @@ def design_dmat(self, x, order, l_extra=False, r_extra=False):
         """
         dmat = np.vstack([
             self.dfun(x, order, idx, l_extra=l_extra, r_extra=r_extra)
-            for idx in range(self.include_first_basis,
-                             self.num_spline_bases)
+            for idx in range(self.basis_start, self.num_spline_bases)
         ]).T
         return dmat
 
@@ -714,8 +712,7 @@ def design_imat(self, a, x, order, l_extra=False, r_extra=False):
         """
         imat = np.vstack([
             self.ifun(a, x, order, idx, l_extra=l_extra, r_extra=r_extra)
-            for idx in range(self.include_first_basis,
-                             self.num_spline_bases)
+            for idx in range(self.basis_start, self.num_spline_bases)
         ]).T
         return imat
 
@@ -747,7 +744,7 @@ class NDXSpline:
     def __init__(self, ndim, knots_list, degree_list,
                  l_linear_list=None,
                  r_linear_list=None,
-                 include_first_basis_list=None):
+                 include_first_basis_list=True):
         """Constructor of ndXSpline class
 
         Args: