diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index bd60f3e741..fd0162ad29 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -124,11 +124,13 @@ check-system-debian:
     IMAGE: debian-amd64
     MAKE_CHECK_ARGS: check
 
+# No targets are built here, just tools, docs, and unit tests. This
+# also feeds into the eventual documentation deployment steps later
 build-tools-and-docs-debian:
   <<: *native_build_job_definition
   variables:
     IMAGE: debian-amd64
-    MAKE_CHECK_ARGS: ctags TAGS cscope
+    MAKE_CHECK_ARGS: check-unit check-softfloat ctags TAGS cscope
     CONFIGURE_ARGS: --disable-system --disable-user --enable-docs --enable-tools
   artifacts:
     expire_in: 2 days
diff --git a/.travis.yml b/.travis.yml
index 3b574a5968..5f1dea873e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -119,15 +119,6 @@ after_script:
 
 jobs:
   include:
-    # Just build tools and run minimal unit and softfloat checks
-    - name: "GCC check-unit and check-softfloat"
-      env:
-        - BASE_CONFIG="--enable-tools"
-        - CONFIG="--disable-user --disable-system"
-        - TEST_CMD="make check-unit check-softfloat -j${JOBS}"
-        - CACHE_NAME="${TRAVIS_BRANCH}-linux-gcc-default"
-
-
     # --enable-debug implies --enable-debug-tcg, also runs quite a bit slower
     - name: "GCC debug (main-softmmu)"
       env: