diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 27e45a0..e0dbc2a 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -23,11 +23,13 @@ jobs:
       - name: Build and run tests
         run: bash .github/build.sh
 
-      # Trigger testing of more linux flavors
-      - name: Trigger linux flavors build
-        uses: peter-evans/repository-dispatch@v2
-        with:
-          event-type: build-linux-flavors
+      # Don't do it this way.  This causes the main badge to
+      # go red if one of the flavors fails.
+      ## Trigger testing of more linux flavors
+      #- name: Trigger linux flavors build
+      #  uses: peter-evans/repository-dispatch@v2
+      #  with:
+      #    event-type: build-linux-flavors
 
   build-and-test-windows:
     #if: false  # Temporarily disable
@@ -90,7 +92,7 @@ jobs:
         shell: cmd
 
   build-and-test-osx:
-    name: Build And Test for OSX
+    name: Build And Test MacOS
     runs-on: macos-latest
     steps:
     - uses: actions/checkout@v3
diff --git a/.github/workflows/linux-flavors.yml b/.github/workflows/linux-flavors.yml
index 263eded..fb4712e 100644
--- a/.github/workflows/linux-flavors.yml
+++ b/.github/workflows/linux-flavors.yml
@@ -4,10 +4,14 @@ name: Linux flavors
 
 # Triggered from the main CI build workflow
 on:
-  workflow_call:
-  workflow_dispatch:
-  repository_dispatch:
-    types: [ build-linux-flavors ]
+  workflow_run:
+    workflows: ["CI"]
+    types:
+      - completed
+  #workflow_call:
+  #workflow_dispatch:
+  #repository_dispatch:
+  #  types: [ build-linux-flavors ]
 
 jobs:
 
diff --git a/README.md b/README.md
index 22bbf83..b64f475 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,5 @@
-# GameNetworkingSockets [![Build Status](https://github.com/ValveSoftware/GameNetworkingSockets/workflows/CI/badge.svg)](https://github.com/ValveSoftware/GameNetworkingSockets/actions)
+# GameNetworkingSockets
+[![Windows, Ubuntu, OSX](https://github.com/ValveSoftware/GameNetworkingSockets/actions/workflows/build.yml/badge.svg)](https://github.com/ValveSoftware/GameNetworkingSockets/actions) [![Linux flavors](https://github.com/ValveSoftware/GameNetworkingSockets/actions/workflows/linux-flavors.yml/badge.svg)](https://github.com/ValveSoftware/GameNetworkingSockets/actions)
 
 GameNetworkingSockets is a basic transport layer for games.  The features are: