diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 0fd352f7..2db0c12f 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -17,14 +17,14 @@ jobs:
           - FLASK_VERSION=0.11.1
           - FLASK_VERSION=0.12.4
           - FLASK_VERSION=1.0.2
-          - TWISTED_VERSION=15.5.0
-          - TWISTED_VERSION=16.1.0
-          - TWISTED_VERSION=16.2.0
-          - TWISTED_VERSION=16.3.0
-          - TWISTED_VERSION=16.4.0
-          - TWISTED_VERSION=16.5.0
-          - TWISTED_VERSION=16.6.0
-          - TWISTED_VERSION=17.1.0
+          - TWISTED_VERSION=15.5.0 treq==15.1.0
+          - TWISTED_VERSION=16.1.0 treq==16.12.0
+          - TWISTED_VERSION=16.2.0 treq==16.12.0
+          - TWISTED_VERSION=16.3.0 treq==16.12.0
+          - TWISTED_VERSION=16.4.0 treq==17.8.0
+          - TWISTED_VERSION=16.5.0 treq==17.8.0
+          - TWISTED_VERSION=16.6.0 treq==17.8.0
+          - TWISTED_VERSION=17.1.0 treq==20.4.1
           - DJANGO_VERSION=1.11.20
           - DJANGO_VERSION=2.0.13
           - DJANGO_VERSION=2.1.7
@@ -48,6 +48,44 @@ jobs:
             framework: DJANGO_VERSION=2.1.15
           - python-version: 3.7
             framework: DJANGO_VERSION=2.1.15
+
+          # twisted/treq setup.py allows:
+          # Twisted < 18.7.0 on python < 3.7
+          # Twisted >= 18.7.0 on python >= 3.7
+          # So we put twisted < 18.x in the matrix
+          # and disallow python 3.7 and 3.8 here.
+          - python-version: 3.7
+            framework: TWISTED_VERSION=15.5.0 treq==15.1.0
+          - python-version: 3.7
+            framework: TWISTED_VERSION=16.1.0 treq==16.12.0
+          - python-version: 3.7
+            framework: TWISTED_VERSION=16.2.0 treq==16.12.0
+          - python-version: 3.7
+            framework: TWISTED_VERSION=16.3.0 treq==16.12.0
+          - python-version: 3.7
+            framework: TWISTED_VERSION=16.4.0 treq==17.8.0
+          - python-version: 3.7
+            framework: TWISTED_VERSION=16.5.0 treq==17.8.0
+          - python-version: 3.7
+            framework: TWISTED_VERSION=16.6.0 treq==17.8.0
+          - python-version: 3.7
+            framework: TWISTED_VERSION=17.1.0 treq==20.4.1
+          - python-version: 3.8
+            framework: TWISTED_VERSION=15.5.0 treq==15.1.0
+          - python-version: 3.8
+            framework: TWISTED_VERSION=16.1.0 treq==16.12.0
+          - python-version: 3.8
+            framework: TWISTED_VERSION=16.2.0 treq==16.12.0
+          - python-version: 3.8
+            framework: TWISTED_VERSION=16.3.0 treq==16.12.0
+          - python-version: 3.8
+            framework: TWISTED_VERSION=16.4.0 treq==17.8.0
+          - python-version: 3.8
+            framework: TWISTED_VERSION=16.5.0 treq==17.8.0
+          - python-version: 3.8
+            framework: TWISTED_VERSION=16.6.0 treq==17.8.0
+          - python-version: 3.8
+            framework: TWISTED_VERSION=17.1.0 treq==20.4.1
         include:
           - python-version: 2.7
             framework: FLASK_VERSION=0.9
@@ -77,9 +115,18 @@ jobs:
             framework: DJANGO_VERSION=1.9.13
           - python-version: 3.5
             framework: DJANGO_VERSION=1.10.8
+          - python-version: 3.7
+            framework: TWISTED_VERSION=18.9.0 treq==20.4.1
+          - python-version: 3.7
+            framework: TWISTED_VERSION=19.10.0 treq==20.4.1
+          - python-version: 3.7
+            framework: TWISTED_VERSION=20.3.0 treq==20.4.1
           - python-version: 3.8
-            framework: TWISTED_VERSION=20.3.0
-
+            framework: TWISTED_VERSION=18.9.0 treq==20.4.1
+          - python-version: 3.8
+            framework: TWISTED_VERSION=19.10.0 treq==20.4.1
+          - python-version: 3.8
+            framework: TWISTED_VERSION=20.3.0 treq==20.4.1
     steps:
       - uses: actions/checkout@v2
         with:
@@ -106,7 +153,7 @@ jobs:
 
       - name: Install Twisted
         if: ${{ contains(matrix.framework, 'TWISTED_VERSION') }}
-        run: pip install Twisted==$TWISTED_VERSION treq==20.4.1
+        run: pip install Twisted==$TWISTED_VERSION idna==2.10
 
       - name: Install Django
         if: ${{ contains(matrix.framework, 'DJANGO_VERSION') }}