diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index bf331d8..f18e5fc 100755
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -60,7 +60,7 @@ jobs:
           install: |
             apt-get update
             apt-get install -y --no-install-recommends python3 python3-pip
-            pip3 install -U pip pytest numpy cotengra
+            pip3 install -U pip pytest # numpy cotengra
           run: |
             set -e
             pip3 install cotengrust --find-links dist --force-reinstall
diff --git a/tests/test_cotengrust.py b/tests/test_cotengrust.py
index f1c8907..7357fb7 100644
--- a/tests/test_cotengrust.py
+++ b/tests/test_cotengrust.py
@@ -1,10 +1,33 @@
 import pytest
-import numpy as np
-from numpy.testing import assert_allclose
-import cotengra as ctg
+
+try:
+    import cotengra as ctg
+
+    ctg_missing = False
+except ImportError:
+    ctg_missing = True
+    ctg = None
+
 import cotengrust as ctgr
 
 
+requires_cotengra = pytest.mark.skipif(ctg_missing, reason="requires cotengra")
+
+
+@pytest.mark.parametrize("which", ["greedy", "optimal"])
+def test_basic_call(which):
+    inputs = [('a', 'b'), ('b', 'c'), ('c', 'd'), ('d', 'a')]
+    output = ('b', 'd')
+    size_dict = {'a': 2, 'b': 3, 'c': 4, 'd': 5}
+    path = {
+        "greedy": ctgr.optimize_greedy,
+        "optimal": ctgr.optimize_optimal,
+    }[
+        which
+    ](inputs, output, size_dict)
+    assert all(len(con) <= 2 for con in path)
+
+
 def find_output_str(lhs):
     tmp_lhs = lhs.replace(",", "")
     return "".join(s for s in sorted(set(tmp_lhs)) if tmp_lhs.count(s) == 1)
@@ -21,20 +44,16 @@ def eq_to_inputs_output(eq):
 
 
 def get_rand_size_dict(inputs, d_min=2, d_max=3):
+    import random
+
     size_dict = {}
     for term in inputs:
         for ix in term:
             if ix not in size_dict:
-                size_dict[ix] = np.random.randint(d_min, d_max + 1)
+                size_dict[ix] = random.randint(d_min, d_max)
     return size_dict
 
 
-def build_arrays(inputs, size_dict):
-    return [
-        np.random.randn(*[size_dict[ix] for ix in term]) for term in inputs
-    ]
-
-
 # these are taken from opt_einsum
 test_case_eqs = [
     # Test scalar-like operations
@@ -120,13 +139,12 @@ def build_arrays(inputs, size_dict):
 ]
 
 
+@requires_cotengra
 @pytest.mark.parametrize("eq", test_case_eqs)
 @pytest.mark.parametrize("which", ["greedy", "optimal"])
 def test_manual_cases(eq, which):
     inputs, output = eq_to_inputs_output(eq)
     size_dict = get_rand_size_dict(inputs)
-    arrays = build_arrays(inputs, size_dict)
-    expected = np.einsum(eq, *arrays, optimize=True)
     path = {
         "greedy": ctgr.optimize_greedy,
         "optimal": ctgr.optimize_optimal,
@@ -134,10 +152,13 @@ def test_manual_cases(eq, which):
         which
     ](inputs, output, size_dict)
     assert all(len(con) <= 2 for con in path)
-    tree = ctg.ContractionTree.from_path(inputs, output, size_dict, path=path)
-    assert_allclose(tree.contract(arrays), expected)
+    tree = ctg.ContractionTree.from_path(
+        inputs, output, size_dict, path=path, check=True
+    )
+    assert tree.is_complete()
 
 
+@requires_cotengra
 @pytest.mark.parametrize("seed", range(10))
 @pytest.mark.parametrize("which", ["greedy", "optimal"])
 def test_basic_rand(seed, which):
@@ -151,8 +172,6 @@ def test_basic_rand(seed, which):
         d_max=3,
         seed=seed,
     )
-    eq = ",".join(map("".join, inputs)) + "->" + "".join(output)
-
     path = {
         "greedy": ctgr.optimize_greedy,
         "optimal": ctgr.optimize_optimal,
@@ -160,13 +179,13 @@ def test_basic_rand(seed, which):
         which
     ](inputs, output, size_dict)
     assert all(len(con) <= 2 for con in path)
-    tree = ctg.ContractionTree.from_path(inputs, output, size_dict, path=path)
-    arrays = [np.random.randn(*s) for s in shapes]
-    assert_allclose(
-        tree.contract(arrays), np.einsum(eq, *arrays, optimize=True)
+    tree = ctg.ContractionTree.from_path(
+        inputs, output, size_dict, path=path, check=True
     )
+    assert tree.is_complete()
 
 
+@requires_cotengra
 def test_optimal_lattice_eq():
     inputs, output, _, size_dict = ctg.utils.lattice_equation(
         [4, 5], d_max=3, seed=42