diff --git a/ci/build_wheel.sh b/ci/build_wheel.sh
index 385a5da20..80685c6a8 100755
--- a/ci/build_wheel.sh
+++ b/ci/build_wheel.sh
@@ -33,7 +33,14 @@ rapids-generate-version > ./VERSION
 
 RAPIDS_PY_CUDA_SUFFIX="$(rapids-wheel-ctk-name-gen ${RAPIDS_CUDA_VERSION})"
 
-cd "${package_dir}"
+touch /tmp/build-constraints.txt
+
+if [[ "${package_name}" == "cuspatial" ]]; then
+  # Downloads libcuspatial wheel from this current build,
+  # then ensures 'cuspatial' wheel builds always use the 'libcuspatial' just built in the same CI run.
+  RAPIDS_PY_WHEEL_NAME="libcuspatial_${RAPIDS_PY_CUDA_SUFFIX}" rapids-download-wheels-from-s3 cpp /tmp/libcuspatial_dist
+  echo "libcuspatial-${RAPIDS_PY_CUDA_SUFFIX} @ file://$(echo /tmp/libcuspatial_dist/libcuspatial_*.whl)" > /tmp/constraints-build.txt
+fi
 
 rapids-logger "Generating build requirements"
 declare -r matrix_selectors="cuda=${RAPIDS_CUDA_VERSION%.*};arch=$(arch);py=${RAPIDS_PY_VERSION};cuda_suffixed=true"
@@ -54,8 +61,11 @@ rapids-logger "Installing build requirements"
 python -m pip install \
     -v \
     --prefer-binary \
+    --constraint /tmp/constraints-build.txt \
     -r /tmp/requirements-build.txt
 
+cd "${package_dir}"
+
 rapids-logger "Building '${package_name}' wheel"
 python -m pip wheel \
     -w dist \
diff --git a/ci/build_wheel_cuspatial.sh b/ci/build_wheel_cuspatial.sh
index e581a3e76..171bfa6a4 100755
--- a/ci/build_wheel_cuspatial.sh
+++ b/ci/build_wheel_cuspatial.sh
@@ -3,15 +3,4 @@
 
 set -euo pipefail
 
-RAPIDS_PY_CUDA_SUFFIX="$(rapids-wheel-ctk-name-gen ${RAPIDS_CUDA_VERSION})"
-
-# Downloads libcuspatial wheel from this current build,
-# then ensures 'cuspatial' wheel builds always use the 'libcuspatial' just built in the same CI run.
-#
-# Using env variable PIP_CONSTRAINT is necessary to ensure the constraints
-# are used when creating the isolated build environment.
-RAPIDS_PY_WHEEL_NAME="libcuspatial_${RAPIDS_PY_CUDA_SUFFIX}" rapids-download-wheels-from-s3 cpp /tmp/libcuspatial_dist
-echo "libcuspatial-${RAPIDS_PY_CUDA_SUFFIX} @ file://$(echo /tmp/libcuspatial_dist/libcuspatial_*.whl)" > /tmp/constraints.txt
-export PIP_CONSTRAINT="/tmp/constraints.txt"
-
 ci/build_wheel.sh cuspatial python/cuspatial python