diff --git a/lib/rules/no-inner-html.js b/lib/rules/no-inner-html.js
index 24b30f1..4a4330e 100644
--- a/lib/rules/no-inner-html.js
+++ b/lib/rules/no-inner-html.js
@@ -30,7 +30,7 @@ module.exports = {
 
     function mightBeHTMLElement(node) {
       const type = astUtils.getNodeTypeAsString(fullTypeChecker, node, context);
-      return type.match(/HTML.*Element/) || type === "any";
+      return type.match(/HTML.*Element/) || type === "any" || type == "Element";
     }
 
     return {
diff --git a/lib/rules/no-postmessage-star-origin.js b/lib/rules/no-postmessage-star-origin.js
index 5a76c0e..680e5ae 100644
--- a/lib/rules/no-postmessage-star-origin.js
+++ b/lib/rules/no-postmessage-star-origin.js
@@ -9,6 +9,10 @@
 
 const astUtils = require("../ast-utils");
 
+function isWindowOrAny(type) {
+  return type === "any" || type === "Window";
+}
+
 module.exports = {
   meta: {
     type: "suggestion",
@@ -41,7 +45,12 @@ module.exports = {
           );
           const tsType = fullTypeChecker.getTypeAtLocation(tsNode);
           const type = fullTypeChecker.typeToString(tsType);
-          if (type !== "any" && type !== "Window") {
+          // Remove some false positives by returning if the type does not contain Window or any
+          if (tsType.isUnionOrIntersection()) {
+            if (tsType.types.every((t) => !isWindowOrAny(fullTypeChecker.typeToString(t)))) {
+              return;
+            }
+          } else if (!isWindowOrAny(type)) {
             return;
           }
         }