diff --git a/.ci/image/Dockerfile.msvc b/.ci/image/Dockerfile
similarity index 85%
rename from .ci/image/Dockerfile.msvc
rename to .ci/image/Dockerfile
index 864dc73..4e3433b 100644
--- a/.ci/image/Dockerfile.msvc
+++ b/.ci/image/Dockerfile
@@ -26,10 +26,38 @@ RUN set -eux; \
         --accept-license \
         splat \
         --output /xwin; \
-    rm -rf \
-        /root/.xwin-cache;
+    # Even though this build step only exists temporary, to copy the
+    # final data out of, it still generates a cache entry on the Docker host.
+    # And to keep that to a minimum, we still delete the stuff we don't need.
+    rm -rf /root/.xwin-cache;
 
-FROM dtmt-ci-base-linux as final
+FROM rust:slim-bullseye as linux
+
+RUN set -eux; \
+    apt-get update; \
+    apt-get install --no-install-recommends -y \
+        build-essential \
+        curl \
+        git \
+        gpg \
+        jq \
+        libatk1.0-dev \
+        libclang-13-dev \
+        libglib2.0-dev \
+        libgtk-3-dev \
+        libpango1.0-dev \
+        libssl-dev \
+        libzstd-dev \
+        pkg-config; \
+    apt-get remove -y --auto-remove; \
+    rm -rf /var/lib/apt/lists/*; \
+    rustup default nightly
+
+WORKDIR /src/dtmt
+
+COPY lib/oodle/*.so lib/oodle/*.a /src/
+
+FROM linux as msvc
 
 ENV KEYRINGS /usr/local/share/keyrings
 
diff --git a/.ci/image/Dockerfile.linux b/.ci/image/Dockerfile.linux
deleted file mode 100644
index 5cbaf5d..0000000
--- a/.ci/image/Dockerfile.linux
+++ /dev/null
@@ -1,25 +0,0 @@
-FROM rust:slim-bullseye
-
-RUN set -eux; \
-    apt-get update; \
-    apt-get install --no-install-recommends -y \
-        build-essential \
-        curl \
-        git \
-        gpg \
-        jq \
-        libatk1.0-dev \
-        libclang-13-dev \
-        libglib2.0-dev \
-        libgtk-3-dev \
-        libpango1.0-dev \
-        libssl-dev \
-        libzstd-dev \
-        pkg-config; \
-    apt-get remove -y --auto-remove; \
-    rm -rf /var/lib/apt/lists/*; \
-    rustup default nightly
-
-WORKDIR /src/dtmt
-
-COPY lib/oodle/*.so lib/oodle/*.a /src/
diff --git a/Justfile b/Justfile
index 967619b..f9b37bc 100644
--- a/Justfile
+++ b/Justfile
@@ -16,16 +16,15 @@ build-image-msvc:
 build-image-linux:
     docker build -f .ci/Dockerfile.linux .
 
-ci-image: ci-image-msvc ci-image-linux
-
-ci-image-msvc:
-    docker build -t dtmt-ci-base-msvc -f .ci/image/Dockerfile.msvc .
+ci-image:
+    # The MSVC image depends on the Linux image. So by building that first,
+    # we actually build both, and cache them, so that "building" the
+    # Linux image afterwards merely needs to pull the cache.
+    docker build --target msvc -t dtmt-ci-base-msvc -f .ci/image/Dockerfile .
+    docker build --target linux -t dtmt-ci-base-linux -f .ci/image/Dockerfile .
     docker tag dtmt-ci-base-msvc registry.sclu1034.dev/dtmt-ci-base-msvc
-    docker push registry.sclu1034.dev/dtmt-ci-base-msvc
-
-ci-image-linux:
-    docker build -t dtmt-ci-base-linux -f .ci/image/Dockerfile.linux .
     docker tag dtmt-ci-base-linux registry.sclu1034.dev/dtmt-ci-base-linux
+    docker push registry.sclu1034.dev/dtmt-ci-base-msvc
     docker push registry.sclu1034.dev/dtmt-ci-base-linux
 
 set-base-pipeline: