diff --git a/tests/integration/test_mixed_space_bayesian_optimization.py b/tests/integration/test_mixed_space_bayesian_optimization.py
index 94d568a69..aa1e0fc46 100644
--- a/tests/integration/test_mixed_space_bayesian_optimization.py
+++ b/tests/integration/test_mixed_space_bayesian_optimization.py
@@ -13,6 +13,7 @@
 # limitations under the License.
 from __future__ import annotations
 
+import dataclasses
 from typing import cast
 
 import numpy as np
@@ -47,6 +48,7 @@
     Box,
     CategoricalSearchSpace,
     DiscreteSearchSpace,
+    EncoderFunction,
     TaggedProductSearchSpace,
     one_hot_encoder,
 )
@@ -167,15 +169,32 @@ def test_optimizer_finds_minima_of_the_scaled_branin_function(
         TensorType, TaggedProductSearchSpace, TrainableProbabilisticModel
     ],
 ) -> None:
-    initial_query_points = mixed_search_space.sample(5)
-    observer = mk_observer(ScaledBranin.objective)
+    mixed_branin = cast(SingleObjectiveTestProblem[TaggedProductSearchSpace], ScaledBranin)
+    _test_optimizer_finds_problem_minima(
+        dataclasses.replace(mixed_branin, search_space=mixed_search_space),
+        num_steps,
+        acquisition_rule,
+    )
+
+
+def _test_optimizer_finds_problem_minima(
+    problem: SingleObjectiveTestProblem[TaggedProductSearchSpace],
+    num_steps: int,
+    acquisition_rule: AcquisitionRule[
+        TensorType, TaggedProductSearchSpace, TrainableProbabilisticModel
+    ],
+    encoder: EncoderFunction | None = None,
+) -> None:
+    initial_query_points = problem.search_space.sample(5)
+    observer = mk_observer(problem.objective)
     initial_data = observer(initial_query_points)
     model = GaussianProcessRegression(
-        build_gpr(initial_data, mixed_search_space, likelihood_variance=1e-8)
+        build_gpr(initial_data, problem.search_space, likelihood_variance=1e-8),
+        encoder=encoder,
     )
 
     dataset = (
-        BayesianOptimizer(observer, mixed_search_space)
+        BayesianOptimizer(observer, problem.search_space)
         .optimize(num_steps, initial_data, model, acquisition_rule)
         .try_get_final_dataset()
     )
@@ -185,7 +204,7 @@ def test_optimizer_finds_minima_of_the_scaled_branin_function(
     best_y = dataset.observations[arg_min_idx]
     best_x = dataset.query_points[arg_min_idx]
 
-    relative_minimizer_err = tf.abs((best_x - ScaledBranin.minimizers) / ScaledBranin.minimizers)
+    relative_minimizer_err = tf.abs((best_x - problem.minimizers) / problem.minimizers)
     # these accuracies are the current best for the given number of optimization steps, which makes
     # this is a regression test
     assert tf.reduce_any(tf.reduce_all(relative_minimizer_err < 0.1, axis=-1), axis=0)
@@ -286,30 +305,10 @@ def test_optimizer_finds_minima_of_the_categorical_scaled_branin_function(
         TensorType, TaggedProductSearchSpace, TrainableProbabilisticModel
     ],
 ) -> None:
-    initial_query_points = cat_problem.search_space.sample(5)
-    observer = mk_observer(cat_problem.objective)
-    initial_data = observer(initial_query_points)
-
     # model uses one-hot encoding for the categorical inputs
-    encoder = one_hot_encoder(cat_problem.search_space)
-    model = GaussianProcessRegression(
-        build_gpr(initial_data, cat_problem.search_space, likelihood_variance=1e-8),
-        encoder=encoder,
-    )
-
-    dataset = (
-        BayesianOptimizer(observer, cat_problem.search_space)
-        .optimize(num_steps, initial_data, model, acquisition_rule)
-        .try_get_final_dataset()
+    _test_optimizer_finds_problem_minima(
+        cat_problem,
+        num_steps,
+        acquisition_rule,
+        encoder=one_hot_encoder(cat_problem.search_space),
     )
-
-    arg_min_idx = tf.squeeze(tf.argmin(dataset.observations, axis=0))
-
-    best_y = dataset.observations[arg_min_idx]
-    best_x = dataset.query_points[arg_min_idx]
-
-    relative_minimizer_err = tf.abs((best_x - cat_problem.minimizers) / cat_problem.minimizers)
-    assert tf.reduce_any(
-        tf.reduce_all(relative_minimizer_err < 0.1, axis=-1), axis=0
-    ), relative_minimizer_err
-    npt.assert_allclose(best_y, cat_problem.minimum, rtol=0.005)
diff --git a/tests/unit/acquisition/test_rule.py b/tests/unit/acquisition/test_rule.py
index 130ca9ebd..f07d280f1 100644
--- a/tests/unit/acquisition/test_rule.py
+++ b/tests/unit/acquisition/test_rule.py
@@ -2337,7 +2337,7 @@ def test_trust_region_discrete_update_size(
 
     # Check the new set of neighbors.
     if categorical:
-        # Hammond distance
+        # Hamming distance
         neighbors_mask = tf.where(search_space.points != tr.location, 1, 0)
         neighbors_mask = tf.reduce_sum(neighbors_mask, axis=-1) <= tr.eps
     else:
diff --git a/trieste/acquisition/rule.py b/trieste/acquisition/rule.py
index 80d03697f..9719e0dd1 100644
--- a/trieste/acquisition/rule.py
+++ b/trieste/acquisition/rule.py
@@ -2280,7 +2280,7 @@ def _compute_global_distances(self) -> TensorType:
             return tf.math.reduce_sum(
                 tf.where(tf.expand_dims(points, -2) == tf.expand_dims(points, -3), 0, 1),
                 axis=-1,
-                keepdims=True,  # (keep last dim for distance calculation below)
+                keepdims=True,  # (keep last dim for reduce_all distance calculation below)
             )  # [num_points, num_points, 1]
         else:
             return tf.abs(