diff --git a/ci-conda.Dockerfile b/ci-conda.Dockerfile
index 5b62b27..e9a68fd 100644
--- a/ci-conda.Dockerfile
+++ b/ci-conda.Dockerfile
@@ -10,7 +10,6 @@ FROM nvidia/cuda:${CUDA_VER}-base-${LINUX_VER} AS miniforge-cuda
 
 ARG LINUX_VER
 ARG PYTHON_VER
-ARG PYTHON_VER_UPPER_BOUND
 ARG DEBIAN_FRONTEND=noninteractive
 ENV PATH=/opt/conda/bin:$PATH
 ENV PYTHON_VERSION=${PYTHON_VER}
@@ -36,7 +35,17 @@ umask 002
 # an older conda with newer packages still works well
 conda update --all -y -n base
 # install expected Python version
-conda install -y -n base "python>=${PYTHON_VERSION},<${PYTHON_VER_UPPER_BOUND}=*_cpython"
+PYTHON_MAJOR_VERSION=${PYTHON_VERSION%%.*}
+PYTHON_MINOR_VERSION=${PYTHON_VERSION#*.}
+PYTHON_UPPER_BOUND="${PYTHON_MAJOR_VERSION}.$((PYTHON_MINOR_VERSION+1)).0a0"
+PYTHON_MINOR_PADDED=$(printf "%02d" "$PYTHON_MINOR_VERSION")
+PYTHON_VERSION_PADDED="${PYTHON_MAJOR_VERSION}.${PYTHON_MINOR_PADDED}"
+if [[ "$PYTHON_VERSION_PADDED" > "3.12" ]]; then
+    PYTHON_ABI_TAG="cp${PYTHON_MAJOR_VERSION}${PYTHON_MINOR_VERSION}"
+else
+    PYTHON_ABI_TAG="cpython"
+fi
+conda install -y -n base "python>=${PYTHON_VERSION},<${PYTHON_UPPER_BOUND}=*_${PYTHON_ABI_TAG}"
 conda update --all -y -n base
 if [[ "$LINUX_VER" == "rockylinux"* ]]; then
   yum install -y findutils
@@ -214,6 +223,18 @@ RUN cat /tmp/condarc.tmpl | envsubst | tee /opt/conda/.condarc; \
 
 # Install CI tools using mamba
 RUN <<EOF
+PYTHON_MAJOR_VERSION=${PYTHON_VERSION%%.*}
+PYTHON_MINOR_VERSION=${PYTHON_VERSION#*.}
+PYTHON_UPPER_BOUND="${PYTHON_MAJOR_VERSION}.$((PYTHON_MINOR_VERSION+1)).0a0"
+PYTHON_MINOR_PADDED=$(printf "%02d" "$PYTHON_MINOR_VERSION")
+PYTHON_VERSION_PADDED="${PYTHON_MAJOR_VERSION}.${PYTHON_MINOR_PADDED}"
+if [[ "$PYTHON_VERSION_PADDED" > "3.12" ]]; then
+    PYTHON_ABI_TAG="cp${PYTHON_MAJOR_VERSION}${PYTHON_MINOR_VERSION}"
+else
+    PYTHON_ABI_TAG="cpython"
+fi
+
+# rust is needed for source builds of codecov-cli -- binaries are not available for Python 3.13 yet.
 rapids-mamba-retry install -y \
   anaconda-client \
   ca-certificates \
@@ -224,9 +245,10 @@ rapids-mamba-retry install -y \
   git \
   jq \
   packaging \
-  "python>=${PYTHON_VERSION},<${PYTHON_VER_UPPER_BOUND}=*_cpython" \
+  "python>=${PYTHON_VERSION},<${PYTHON_UPPER_BOUND}=*_${PYTHON_ABI_TAG}" \
   "rapids-dependency-file-generator==1.*" \
   rattler-build \
+  rust \
 ;
 conda clean -aipty
 EOF
diff --git a/ci/compute-build-args.sh b/ci/compute-build-args.sh
index 95797d2..8c5ede2 100755
--- a/ci/compute-build-args.sh
+++ b/ci/compute-build-args.sh
@@ -17,11 +17,6 @@ if [[
   MANYLINUX_VER="manylinux_2_31"
 fi
 
-# compute upper bound, e.g. "3.11 -> 3.12.0a0"
-PYTHON_VER_MAJOR="${PYTHON_VER%%.*}"
-PYTHON_VER_MINOR="${PYTHON_VER#*.}"
-PYTHON_VER_UPPER_BOUND="${PYTHON_VER_MAJOR}.$(( PYTHON_VER_MINOR + 1)).0a0"
-
 # translate ARCH to conda-equivalent string values
 CONDA_ARCH=$(echo "$ARCH" | sed 's#amd64#linux64#' | sed 's#arm64#aarch64#')
 
@@ -29,7 +24,6 @@ ARGS="
 CUDA_VER: ${CUDA_VER}
 LINUX_VER: ${LINUX_VER}
 PYTHON_VER: ${PYTHON_VER}
-PYTHON_VER_UPPER_BOUND: ${PYTHON_VER_UPPER_BOUND}
 CPU_ARCH: ${ARCH}
 REAL_ARCH: $(arch)
 MANYLINUX_VER: ${MANYLINUX_VER}
diff --git a/matrix.yaml b/matrix.yaml
index f5db6d3..47de835 100644
--- a/matrix.yaml
+++ b/matrix.yaml
@@ -9,6 +9,7 @@ PYTHON_VER:
   - "3.10"
   - "3.11"
   - "3.12"
+  - "3.13"
 LINUX_VER:
   - "ubuntu20.04"
   - "ubuntu22.04"