diff --git a/src/ci/docker/host-x86_64/x86_64-gnu-pre-stabilization/Dockerfile b/src/ci/docker/host-x86_64/x86_64-gnu-next-trait-solver-polonius/Dockerfile
similarity index 78%
rename from src/ci/docker/host-x86_64/x86_64-gnu-pre-stabilization/Dockerfile
rename to src/ci/docker/host-x86_64/x86_64-gnu-next-trait-solver-polonius/Dockerfile
index 8b61470aeb5f1..4198092640bfb 100644
--- a/src/ci/docker/host-x86_64/x86_64-gnu-pre-stabilization/Dockerfile
+++ b/src/ci/docker/host-x86_64/x86_64-gnu-next-trait-solver-polonius/Dockerfile
@@ -25,5 +25,5 @@ RUN sh /scripts/sccache.sh
 
 ENV RUST_CONFIGURE_ARGS="--build=x86_64-unknown-linux-gnu"
 
-COPY scripts/x86_64-gnu-pre-stabilization.sh /scripts/
-ENV SCRIPT="/scripts/x86_64-gnu-pre-stabilization.sh"
+COPY scripts/x86_64-gnu-next-trait-solver-polonius.sh /scripts/
+ENV SCRIPT="/scripts/x86_64-gnu-next-trait-solver-polonius.sh"
diff --git a/src/ci/docker/scripts/x86_64-gnu-pre-stabilization.sh b/src/ci/docker/scripts/x86_64-gnu-next-trait-solver-polonius.sh
similarity index 75%
rename from src/ci/docker/scripts/x86_64-gnu-pre-stabilization.sh
rename to src/ci/docker/scripts/x86_64-gnu-next-trait-solver-polonius.sh
index 81c1c4356c342..9d1bc8d409e7b 100755
--- a/src/ci/docker/scripts/x86_64-gnu-pre-stabilization.sh
+++ b/src/ci/docker/scripts/x86_64-gnu-next-trait-solver-polonius.sh
@@ -5,12 +5,14 @@ set -ex
 # This script tests features intended to be stabilized in 2026. We want to
 # ensure they don't regress until then.
 
-# 1. For the new trait solver, we want to:
+# 1. For the next trait solver, we want to:
 # - ensure it can build the standard library
+# - ensure it actually bootstraps
 #
-# FIXME: we also need to ensure it actually bootstraps.
+# We test both by building the _stage 2_ library with the next solver enabled
+# at stage 1 via rustflags.
 
-RUSTFLAGS_NOT_BOOTSTRAP="-Znext-solver=globally" ../x build library --stage 1
+RUSTFLAGS_NOT_BOOTSTRAP="-Znext-solver=globally" ../x build library --stage 2
 
 # 2. For the polonius alpha, we run the UI tests under the polonius
 # compare-mode.
diff --git a/src/ci/github-actions/jobs.yml b/src/ci/github-actions/jobs.yml
index 2f92a30065b1f..25593f1ea238f 100644
--- a/src/ci/github-actions/jobs.yml
+++ b/src/ci/github-actions/jobs.yml
@@ -159,8 +159,8 @@ pr:
   
   # This job tests features we want to stabilize soon, to ensure they don't
   # regress.
-  - name: x86_64-gnu-pre-stabilization
-    doc_url: https://rustc-dev-guide.rust-lang.org/tests/pre-stabilization-ci-job.html
+  - name: x86_64-gnu-next-trait-solver-polonius
+    doc_url: https://rustc-dev-guide.rust-lang.org/tests/x86_64-gnu-next-trait-solver-polonius-ci-job.html
     env:
       CODEGEN_BACKENDS: llvm
     <<: *job-linux-4c