diff --git a/.github/actions/windows-tests/action.yml b/.github/actions/windows-tests/action.yml
index 0eeb6f9003a7..d856c7f5de29 100644
--- a/.github/actions/windows-tests/action.yml
+++ b/.github/actions/windows-tests/action.yml
@@ -29,8 +29,11 @@ runs:
         architecture: ${{ inputs.arch }}
         cache: pip
         cache-dependency-path: ci-constraints-requirements.txt
+    # llvm-tools is only used to process Rust coverage data, which the
+    # tests-nocoverage session doesn't collect.
     - run: rustup component add llvm-tools-preview
       shell: bash
+      if: ${{ inputs.noxsession != 'tests-nocoverage' }}
     - name: Cache rust and pip
       uses: ./.github/actions/cache
       with:
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 5c6132cdb039..5a7df5da3914 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -79,8 +79,10 @@ jobs:
           components: rustfmt,clippy
         if: matrix.PYTHON.RUST
 
+      # llvm-tools is only used to process Rust coverage data, which the
+      # tests-nocoverage session doesn't collect.
       - run: rustup component add llvm-tools-preview
-        if: matrix.PYTHON.NOXSESSION != 'flake' && matrix.PYTHON.NOXSESSION != 'docs'
+        if: matrix.PYTHON.NOXSESSION != 'flake' && matrix.PYTHON.NOXSESSION != 'docs' && matrix.PYTHON.NOXSESSION != 'tests-nocoverage'
       - name: Clone test vectors
         timeout-minutes: 2
         uses: ./.github/actions/fetch-vectors