diff --git a/src/ecdsa/test_ecdsa.py b/src/ecdsa/test_ecdsa.py
index dbc4a6eb..2af527b6 100644
--- a/src/ecdsa/test_ecdsa.py
+++ b/src/ecdsa/test_ecdsa.py
@@ -622,12 +622,12 @@ def st_random_gen_key_msg_nonce(draw):
     name = draw(st.sampled_from(sorted(name_gen.keys())))
     note("Generator used: {0}".format(name))
     generator = name_gen[name]
-    order = int(generator.order())
+    order = int(generator.order()) - 1
 
     key = draw(st.integers(min_value=1, max_value=order))
     msg = draw(st.integers(min_value=1, max_value=order))
     nonce = draw(
-        st.integers(min_value=1, max_value=order + 1)
+        st.integers(min_value=1, max_value=order)
         | st.integers(min_value=order >> 1, max_value=order)
     )
     return generator, key, msg, nonce
diff --git a/src/ecdsa/test_ellipticcurve.py b/src/ecdsa/test_ellipticcurve.py
index 85faef4d..f46fd9ea 100644
--- a/src/ecdsa/test_ellipticcurve.py
+++ b/src/ecdsa/test_ellipticcurve.py
@@ -44,7 +44,7 @@
 
 
 @settings(**HYP_SLOW_SETTINGS)
-@given(st.integers(min_value=1, max_value=r + 1))
+@given(st.integers(min_value=1, max_value=r - 1))
 def test_p192_mult_tests(multiple):
     inv_m = inverse_mod(multiple, r)
 
diff --git a/src/ecdsa/test_jacobi.py b/src/ecdsa/test_jacobi.py
index 1f528048..71fb33e5 100644
--- a/src/ecdsa/test_jacobi.py
+++ b/src/ecdsa/test_jacobi.py
@@ -202,7 +202,7 @@ def test_compare_double_with_multiply(self):
     @settings(max_examples=10)
     @given(
         st.integers(
-            min_value=0, max_value=int(generator_brainpoolp160r1.order())
+            min_value=0, max_value=int(generator_brainpoolp160r1.order() - 1)
         )
     )
     def test_multiplications(self, mul):
@@ -217,7 +217,7 @@ def test_multiplications(self, mul):
     @settings(max_examples=10)
     @given(
         st.integers(
-            min_value=0, max_value=int(generator_brainpoolp160r1.order())
+            min_value=0, max_value=int(generator_brainpoolp160r1.order() - 1)
         )
     )
     @example(0)
@@ -235,10 +235,10 @@ def test_precompute(self, mul):
     @settings(max_examples=10)
     @given(
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
     )
     @example(3, 3)
@@ -254,10 +254,10 @@ def test_add_scaled_points(self, a_mul, b_mul):
     @settings(max_examples=10)
     @given(
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
         st.integers(min_value=1, max_value=int(curve_brainpoolp160r1.p() - 1)),
     )
@@ -286,10 +286,10 @@ def test_add_one_scaled_point(self, a_mul, b_mul, new_z):
     @settings(max_examples=10)
     @given(
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
         st.integers(min_value=1, max_value=int(curve_brainpoolp160r1.p() - 1)),
     )
@@ -351,10 +351,10 @@ def test_add_same_scale_points_static(self):
     @settings(max_examples=14)
     @given(
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
         st.integers(
-            min_value=1, max_value=int(generator_brainpoolp160r1.order())
+            min_value=1, max_value=int(generator_brainpoolp160r1.order() - 1)
         ),
         st.lists(
             st.integers(