diff --git a/.github/workflows/node-4+.yml b/.github/workflows/node-4+.yml
index 6456762fc..b13e3b88c 100644
--- a/.github/workflows/node-4+.yml
+++ b/.github/workflows/node-4+.yml
@@ -33,6 +33,11 @@ jobs:
           - 3
           - 2
         include:
+          - node-version: 'lts/*'
+            eslint: 7
+            ts-parser: 3
+            env:
+              TS_PARSER: 3
           - node-version: 'lts/*'
             eslint: 7
             ts-parser: 2
diff --git a/package.json b/package.json
index d1a6bd5e0..9369f8875 100644
--- a/package.json
+++ b/package.json
@@ -56,7 +56,7 @@
   "devDependencies": {
     "@eslint/import-test-order-redirect-scoped": "file:./tests/files/order-redirect-scoped",
     "@test-scope/some-module": "file:./tests/files/symlinked-module",
-    "@typescript-eslint/parser": "^2.23.0 || ^3.3.0",
+    "@typescript-eslint/parser": "^2.23.0 || ^3.3.0 || ^4.29.3",
     "array.prototype.flatmap": "^1.2.4",
     "babel-cli": "^6.26.0",
     "babel-core": "^6.26.3",
diff --git a/tests/dep-time-travel.sh b/tests/dep-time-travel.sh
index ad00568e4..d6f5aedfc 100755
--- a/tests/dep-time-travel.sh
+++ b/tests/dep-time-travel.sh
@@ -8,10 +8,16 @@ export NPM_CONFIG_LEGACY_PEER_DEPS=true
 
 npm install --no-save "eslint@${ESLINT_VERSION}" --ignore-scripts
 
-# completely remove the new TypeScript parser for ESLint < v5
-if [[ "$ESLINT_VERSION" -lt "5" ]]; then
+
+
+if [[ -n "$TS_PARSER" ]]; then # if TS parser is manually set, always use it
+  echo "Downgrading @typescript-eslint/parser..."
+  npm i --no-save "@typescript-eslint/parser@${TS_PARSER}"
+elif [[ "$ESLINT_VERSION" -lt "5" ]]; then # completely remove the new TypeScript parser for ESLint < v5
   echo "Removing @typescript-eslint/parser..."
   npm uninstall --no-save @typescript-eslint/parser
+elif [[ "$TRAVIS_NODE_VERSION" -lt "10" ]]; then # TS parser 3 requires node 10+
+  npm i --no-save "@typescript-eslint/parser@3"
 fi
 
 # use these alternate TypeScript dependencies for ESLint < v4
@@ -28,8 +34,3 @@ if [[ "$TRAVIS_NODE_VERSION" -lt "8" ]]; then
   echo "Downgrading eslint-import-resolver-typescript..."
   npm i --no-save eslint-import-resolver-typescript@1.0.2
 fi
-
-if [[ -n "$TS_PARSER" ]]; then
-  echo "Downgrading @typescript-eslint/parser..."
-  npm i --no-save @typescript-eslint/parser@2
-fi