diff --git a/.github/workflows/security.yml b/.github/workflows/security.yml
index cdab3d1..6455a4f 100644
--- a/.github/workflows/security.yml
+++ b/.github/workflows/security.yml
@@ -1,6 +1,10 @@
 # Reusable security scan: secrets, dependencies, SAST, configuration,
 # licences, SBOM and (optionally) the container image.
 #
+# A scheduled run (the callers' weekly cron) scans the dependencies and the
+# image only: new advisories against unchanged code show up there. The other
+# scans repeat what the last pull request found (`scheduled-full` runs them).
+#
 # Every scanner job only reports. The `report` job reads all findings,
 # applies the repository's exceptions (security/vex.openvex.json,
 # .trivyignore.yaml, .gitleaks.toml / baseline) and fails when a category in
@@ -133,6 +137,15 @@ on:
         description: Upload results to the Security tab on public repositories.
         type: boolean
         default: true
+      scheduled-full:
+        description: >-
+          A scheduled run scans dependencies and the image only, where new
+          advisories appear without a code change; the secret, SAST,
+          configuration and licence scans and the SBOM ran on the pull request
+          that last changed the code. True runs them on schedule too (the
+          self-test).
+        type: boolean
+        default: false
       harness-ref:
         type: string
         default: v1
@@ -158,7 +171,7 @@ env:
 
 jobs:
   gitleaks:
-    if: inputs.gitleaks
+    if: inputs.gitleaks && (github.event_name != 'schedule' || inputs.scheduled-full)
     runs-on: ubuntu-latest
     timeout-minutes: 15
     permissions:
@@ -298,7 +311,7 @@ jobs:
           category: deps
 
   semgrep:
-    if: inputs.semgrep
+    if: inputs.semgrep && (github.event_name != 'schedule' || inputs.scheduled-full)
     runs-on: ubuntu-latest
     timeout-minutes: 20
     permissions:
@@ -350,7 +363,7 @@ jobs:
           category: semgrep
 
   sbom:
-    if: inputs.languages != '' && inputs.languages != 'none'
+    if: inputs.languages != '' && inputs.languages != 'none' && (github.event_name != 'schedule' || inputs.scheduled-full)
     runs-on: ubuntu-latest
     timeout-minutes: 15
     steps:
@@ -414,7 +427,7 @@ jobs:
           retention-days: 90
 
   config:
-    if: inputs.config-scan
+    if: inputs.config-scan && (github.event_name != 'schedule' || inputs.scheduled-full)
     runs-on: ubuntu-latest
     timeout-minutes: 15
     permissions:
@@ -472,7 +485,7 @@ jobs:
           category: config
 
   licenses:
-    if: inputs.licenses
+    if: inputs.licenses && (github.event_name != 'schedule' || inputs.scheduled-full)
     runs-on: ubuntu-latest
     timeout-minutes: 15
     steps:
diff --git a/.github/workflows/selftest.yml b/.github/workflows/selftest.yml
index 03450a3..3e1ca5c 100644
--- a/.github/workflows/selftest.yml
+++ b/.github/workflows/selftest.yml
@@ -215,6 +215,8 @@ jobs:
       gitleaks-mode: dir
       fail-on: secrets,vuln-critical,vuln-high,misconfig-high,license-forbidden,semgrep-error
       code-scanning: false
+      # Weekly too: every scanner, not only the dependency and image scans.
+      scheduled-full: true
       harness-ref: ${{ github.sha }}
 
   # The Node path of the scan (osv-scanner on the lockfile, trivy SBOM) on a
@@ -232,6 +234,8 @@ jobs:
       gitleaks-mode: dir
       fail-on: secrets,vuln-critical,vuln-high,misconfig-high,license-forbidden,semgrep-error
       code-scanning: false
+      # Weekly too: every scanner, not only the dependency and image scans.
+      scheduled-full: true
       harness-ref: ${{ github.sha }}
 
   security-planted:
@@ -251,6 +255,8 @@ jobs:
       context: tests/fixtures/planted
       image-on: pull_request,push,schedule,workflow_dispatch
       code-scanning: false
+      # Weekly too: every scanner, not only the dependency and image scans.
+      scheduled-full: true
       harness-ref: ${{ github.sha }}
 
   # A chart whose dependency is not committed: trivy skips the whole chart,
@@ -295,6 +301,8 @@ jobs:
       config-setup-recipe: deps
       config-tools: helm
       code-scanning: false
+      # Weekly too: every scanner, not only the dependency and image scans.
+      scheduled-full: true
       harness-ref: ${{ github.sha }}
 
   # Dry run of the release workflow (not the merge of a release pull request:
diff --git a/README.md b/README.md
index c095ff7..efb566c 100644
--- a/README.md
+++ b/README.md
@@ -121,7 +121,9 @@ succeeded (see [templates/workflows/ci-go.yml](templates/workflows/ci-go.yml)).
 
 The check workflows (`ci.yml`, `security.yml`) run on pull requests into
 `main`, plus the weekly security scan; a run after the merge would test the
-same tree again. The version file decides what a pull request is
+same tree again. The weekly scan covers the dependencies and the image only,
+where new advisories appear without a code change (`scheduled-full: true`
+runs every scanner). The version file decides what a pull request is
 (`release-intent.yml`):
 
 | Kind | Made with | Title | Version | On the pull request | After the merge |