diff --git a/ci/coverage_report.sh b/ci/coverage_report.sh
index 222cd80e9..f6ddba087 100755
--- a/ci/coverage_report.sh
+++ b/ci/coverage_report.sh
@@ -12,7 +12,7 @@ echo "Package path: ${package}"
 python -m pip install \
     "${package}" \
     "cuda-python==${CUDA_VER_MAJOR_MINOR%.*}.*" \
-    "cuda-core==0.3.*" \
+    "cuda-core" \
     pytest-cov \
     coverage \
     --group test
diff --git a/ci/test_thirdparty_awkward.sh b/ci/test_thirdparty_awkward.sh
index 8e3c09ea8..1046bf733 100755
--- a/ci/test_thirdparty_awkward.sh
+++ b/ci/test_thirdparty_awkward.sh
@@ -17,7 +17,7 @@ echo "Package path: ${package}"
 python -m pip install \
     "${package}" \
     "cuda-python==${CUDA_VER_MAJOR_MINOR%.*}.*" \
-    "cuda-core==0.3.*" \
+    "cuda-core" \
     "nvidia-nvjitlink-cu12" \
     --group test
 
@@ -27,6 +27,55 @@ git clone --recursive https://github.com/scikit-hep/awkward.git
 pushd awkward
 git checkout v${AWKWARD_VERSION}
 
+# Avoid tests that are unreliable on the CUDA target:
+#
+# - awkward_RecordArray_reduce_nonlocal_outoffsets_64
+# - test_3459_virtualarray_with_cuda
+#
+# as per discussion in https://github.com/scikit-hep/awkward/discussions/3587
+
+
+rapids-logger "Patch awkward tests"
+
+patch -p1 <<'EOF'
+diff --git a/dev/generate-tests.py b/dev/generate-tests.py
+index 1292e0cf..4534a57c 100644
+--- a/dev/generate-tests.py
++++ b/dev/generate-tests.py
+@@ -970,7 +970,6 @@ cuda_kernels_tests = [
+     "awkward_UnionArray_regular_index_getsize",
+     "awkward_UnionArray_simplify",
+     "awkward_UnionArray_simplify_one",
+-    "awkward_RecordArray_reduce_nonlocal_outoffsets_64",
+     "awkward_reduce_count_64",
+     "awkward_reduce_max",
+     "awkward_reduce_max_complex",
+diff --git a/tests-cuda/test_3459_virtualarray_with_cuda.py b/tests-cuda/test_3459_virtualarray_with_cuda.py
+index e2bcab12..c82f63c3 100644
+--- a/tests-cuda/test_3459_virtualarray_with_cuda.py
++++ b/tests-cuda/test_3459_virtualarray_with_cuda.py
+@@ -9,6 +9,7 @@ import awkward as ak
+ from awkward._nplikes.cupy import Cupy
+ from awkward._nplikes.virtual import VirtualNDArray
+
++pytestmark = pytest.mark.skip("temporarily skipping all tests in this module")
+
+ @pytest.fixture(scope="function", autouse=True)
+ def cleanup_cuda():
+diff --git a/tests-cuda/test_3149_complex_reducers.py b/tests-cuda/test_3149_complex_reducers.py
+index 39080a34..0eb3940f 100644
+--- a/tests-cuda/test_3149_complex_reducers.py
++++ b/tests-cuda/test_3149_complex_reducers.py
+@@ -544,6 +544,7 @@ def test_block_boundary_prod_complex12():
+     del cuda_content, cuda_depth1
+
+
++@pytest.mark.skip("Intermittent failures")
+ def test_block_boundary_prod_complex13():
+     rng = np.random.default_rng(seed=42)
+     array = rng.integers(50, size=1000)
+EOF
+
 rapids-logger "Generate awkward tests"
 nox -s prepare -- --tests
 
diff --git a/ci/test_thirdparty_cudf.sh b/ci/test_thirdparty_cudf.sh
index 357b4dd65..66297a7c7 100755
--- a/ci/test_thirdparty_cudf.sh
+++ b/ci/test_thirdparty_cudf.sh
@@ -22,7 +22,7 @@ echo "Package path: ${package}"
 python -m pip install \
     "${package}" \
     "cuda-python==${CUDA_VER_MAJOR_MINOR%.*}.*" \
-    "cuda-core==0.3.*" \
+    "cuda-core" \
     "nvidia-nvjitlink-cu12" \
     --group test
 
diff --git a/ci/test_thirdparty_nvmath.sh b/ci/test_thirdparty_nvmath.sh
index e062b5d93..657606a0a 100755
--- a/ci/test_thirdparty_nvmath.sh
+++ b/ci/test_thirdparty_nvmath.sh
@@ -23,7 +23,7 @@ echo "Package path: ${package}"
 python -m pip install \
     "${package}" \
     "cuda-python==${CUDA_VER_MAJOR_MINOR%.*}.*" \
-    "cuda-core==0.3.*" \
+    "cuda-core" \
     "nvidia-nvjitlink-cu12" \
     --group test