diff --git a/tests/integration/test_mixed_space_bayesian_optimization.py b/tests/integration/test_mixed_space_bayesian_optimization.py
index bc4a7997c..16a9eb78f 100644
--- a/tests/integration/test_mixed_space_bayesian_optimization.py
+++ b/tests/integration/test_mixed_space_bayesian_optimization.py
@@ -15,7 +15,6 @@
 
 from typing import cast
 
-import gpflow
 import numpy as np
 import numpy.testing as npt
 import pytest
@@ -50,6 +49,7 @@
     CategoricalSearchSpace,
     DiscreteSearchSpace,
     TaggedProductSearchSpace,
+    one_hot_encoded_space,
     one_hot_encoder,
 )
 from trieste.types import TensorType
@@ -260,11 +260,9 @@ def test_optimizer_finds_minima_of_the_categorical_scaled_branin_function(
 
     # model uses one-hot encoding for the categorical inputs
     encoder = one_hot_encoder(problem.search_space)
-    kernel = gpflow.kernels.Matern52(
-        variance=tf.math.reduce_variance(initial_data.observations), lengthscales=0.1
-    )
+    encoded_space = one_hot_encoded_space(problem.search_space)
     model = GaussianProcessRegression(
-        build_gpr(encode_dataset(initial_data, encoder), kernel=kernel, likelihood_variance=1e-8),
+        build_gpr(encode_dataset(initial_data, encoder), encoded_space, likelihood_variance=1e-8),
         encoder=encoder,
     )
 
diff --git a/trieste/space.py b/trieste/space.py
index 2ab3d1166..4a228460c 100644
--- a/trieste/space.py
+++ b/trieste/space.py
@@ -518,6 +518,20 @@ def one_hot_encoder(space: SearchSpace) -> EncoderFunction:
     return space.one_hot_encoder if isinstance(space, HasOneHotEncoder) else lambda x: x
 
 
+def one_hot_encoded_space(space: SearchSpace) -> SearchSpace:
+    "A bounded search space corresponding to the one-hot encoding of the given space."
+
+    if isinstance(space, GeneralDiscreteSearchSpace) and isinstance(space, HasOneHotEncoder):
+        return DiscreteSearchSpace(space.one_hot_encoder(space.points))
+    elif isinstance(space, TaggedProductSearchSpace):
+        spaces = [one_hot_encoded_space(space.get_subspace(tag)) for tag in space.subspace_tags]
+        return TaggedProductSearchSpace(spaces=spaces, tags=space.subspace_tags)
+    elif isinstance(space, HasOneHotEncoder):
+        raise NotImplementedError(f"Unsupported one-hot-encoded space {type(space)}")
+    else:
+        return space
+
+
 class CategoricalSearchSpace(GeneralDiscreteSearchSpace, HasOneHotEncoder):
     r"""
     A categorical :class:`SearchSpace` representing a finite set :math:`\mathcal{C}` of categories,