diff --git a/test/qpy_compat/run_tests.sh b/test/qpy_compat/run_tests.sh
index 3717d1c712db..a6ff67b14a94 100755
--- a/test/qpy_compat/run_tests.sh
+++ b/test/qpy_compat/run_tests.sh
@@ -14,6 +14,7 @@
 set -e
 set -o pipefail
 set -x
+shopt -s nullglob
 
 # Set fixed hash seed to ensure set orders are identical between saving and
 # loading.
@@ -23,11 +24,22 @@ echo "PYTHONHASHSEED=$PYTHONHASHSEED"
 our_dir="$(realpath -- "$(dirname -- "${BASH_SOURCE[0]}")")"
 repo_root="$(realpath -- "$our_dir/../..")"
 
+# First, prepare a wheel file for the dev version.  We install several venvs with this, and while
+# cargo will cache some rust artefacts, it still has to re-link each time, so the wheel build takes
+# a little while.
+wheel_dir="$(pwd -P)/wheels"
+python -m pip wheel --no-deps --wheel-dir "$wheel_dir" "$repo_root"
+all_wheels=("$wheel_dir"/*.whl)
+qiskit_dev_wheel="${all_wheels[0]}"
+
+# Now set up a "base" development-version environment, which we'll use for most of the backwards
+# compatibility checks.
 qiskit_venv="$(pwd -P)/venvs/dev"
 qiskit_python="$qiskit_venv/bin/python"
 python -m venv "$qiskit_venv"
+
 # `packaging` is needed for the `get_versions.py` script.
-"$qiskit_venv/bin/pip" install -c "$repo_root/constraints.txt" "$repo_root" packaging
+"$qiskit_venv/bin/pip" install -c "$repo_root/constraints.txt" "$qiskit_dev_wheel" packaging
 
 # Run all of the tests of cross-Qiskit-version compatibility.
 "$qiskit_python" "$our_dir/get_versions.py" | parallel --colsep=" " bash "$our_dir/process_version.sh" -p "$qiskit_python"
@@ -58,7 +70,7 @@ for i in "${!symengine_versions[@]}"; do
     symengine_venv="$symengine_venv_prefix$i"
     files_dir="$symengine_files_prefix$i"
     python -m venv "$symengine_venv"
-    "$symengine_venv/bin/pip" install -c "$repo_root/constraints.txt" "$repo_root" "symengine$specifier"
+    "$symengine_venv/bin/pip" install -c "$repo_root/constraints.txt" "$qiskit_dev_wheel" "symengine$specifier"
     mkdir -p "$files_dir"
     pushd "$files_dir"
     "$symengine_venv/bin/python" -c 'import symengine; print(symengine.__version__)' > "SYMENGINE_VERSION"