diff --git a/docs/getting-started/installation.md b/docs/getting-started/installation.md
index 101b13541ed7..f219a953645a 100644
--- a/docs/getting-started/installation.md
+++ b/docs/getting-started/installation.md
@@ -34,11 +34,11 @@ By default, uv is installed to `~/.cargo/bin`.
 Request a specific version by including it in the URL:
 
 ```console title="macOS and Linux"
-$ curl -LsSf https://astral.sh/uv/0.2.11/install.sh | sh
+$ curl -LsSf https://astral.sh/uv/0.2.37/install.sh | sh
 ```
 
 ```console title="Windows"
-$ powershell -c "irm https://astral.sh/uv/0.2.11/install.ps1 | iex"
+$ powershell -c "irm https://astral.sh/uv/0.2.37/install.ps1 | iex"
 ```
 
 !!! tip
diff --git a/docs/guides/integration/docker.md b/docs/guides/integration/docker.md
index d63af1926422..077eda7887f2 100644
--- a/docs/guides/integration/docker.md
+++ b/docs/guides/integration/docker.md
@@ -18,18 +18,37 @@ FROM python:3.12-slim-bullseye
 COPY --from=ghcr.io/astral-sh/uv:latest /uv /bin/uv
 ```
 
-Or with the standalone installer:
+Or, with the installer:
 
 ```dockerfile title="Dockerfile"
 FROM python:3.12-slim-bullseye
+
+# The installer requires curl (and certificates) to download the release archive
 RUN apt-get update && apt-get install -y --no-install-recommends curl ca-certificates
-RUN curl -LsSf https://astral.sh/uv/install.sh > /tmp/uv-installer.sh && sh /tmp/uv-installer.sh && rm /tmp/uv-installer.sh
+
+# Download the latest installer
+ADD https://astral.sh/uv/install.sh /uv-installer.sh
+
+# Run the installer then remove it
+RUN sh /uv-installer.sh && rm /uv-installer.sh
+
+# Ensure the installed binary is on the `PATH`
 ENV PATH="/root/.cargo/bin/:$PATH"
 ```
 
 Note this requires `curl` to be available.
 
-In either case, it is best practice to pin to a specific uv version.
+In either case, it is best practice to pin to a specific uv version, e.g., with:
+
+```dockerfile
+COPY --from=ghcr.io/astral-sh/uv:0.2.37 /uv /bin/uv
+```
+
+Or, with the installer:
+
+```dockerfile
+ADD https://astral.sh/uv/0.2.37/install.sh /uv-installer.sh
+```
 
 ## Installing a package
 
diff --git a/pyproject.toml b/pyproject.toml
index 054720b5172c..c0b9d28b92f8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -67,6 +67,8 @@ version_files = [
   "README.md",
   "crates/uv/Cargo.toml",
   "crates/uv-version/Cargo.toml",
+  "docs/getting-started/installation.md",
+  "docs/guides/integration/docker.md",
   "docs/guides/integration/pre-commit.md",
   "docs/guides/integration/github.md",
 ]