diff --git a/CHANGELOG.unreleased.md b/CHANGELOG.unreleased.md
index 5de189bd8..914cde909 100644
--- a/CHANGELOG.unreleased.md
+++ b/CHANGELOG.unreleased.md
@@ -325,7 +325,7 @@ export default (function log() {}).toString();
 export default (function log() {} as typeof console.log);
 ```
 
-### TypeScript: Keep necessary parentheses around non-null assertions. ([#6136] by [@sosukesuzuki], [#6140] by [@thorn0])
+### TypeScript: Keep necessary parentheses around non-null assertions. ([#6136] by [@sosukesuzuki], [#6140] by [@thorn0], [#6148] by [@bakkot])
 
 Previously, Prettier removed necessary parentheses around non-null assertions if the result of the assertion expression was called as a constructor.
 
@@ -338,7 +338,29 @@ const b = new (c()!)();
 const b = new c()!();
 
 // Output (Prettier master)
-const b = new (c()!)();
+const b = new (c())!();
+```
+
+### Javascript: Address parentheses bugs for edge cases with call and new. ([#6148] by [@bakkot])
+
+Adding all and only the necessary parentheses when mixing `new` with function calls is tricky. This change fixes two issues where necessary parentheses were omitted and one when redundant parentheses were added.
+
+<!-- prettier-ignore -->
+```ts
+// Input
+new (x()``.y)();
+new (x()!.y)();
+new e[f().x].y()
+
+// Output (Prettier stable)
+new x()``.y();
+new x()!.y();
+new e[(f()).x].y();
+
+// Output (Prettier master)
+new (x())``.y();
+new (x())!.y();
+new e[f().x].y();
 ```
 
 [#5979]: https://github.com/prettier/prettier/pull/5979
@@ -357,6 +379,7 @@ const b = new (c()!)();
 [#6133]: https://github.com/prettier/prettier/pull/6133
 [#6136]: https://github.com/prettier/prettier/pull/6136
 [#6140]: https://github.com/prettier/prettier/pull/6140
+[#6148]: https://github.com/prettier/prettier/pull/6148
 [@belochub]: https://github.com/belochub
 [@brainkim]: https://github.com/brainkim
 [@duailibe]: https://github.com/duailibe
@@ -366,3 +389,4 @@ const b = new (c()!)();
 [@jwbay]: https://github.com/jwbay
 [@sosukesuzuki]: https://github.com/sosukesuzuki
 [@thorn0]: https://github.com/thorn0
+[@bakkot]: https://github.com/bakkot
diff --git a/src/language-js/needs-parens.js b/src/language-js/needs-parens.js
index 74a3ad0e3..09967d9d7 100644
--- a/src/language-js/needs-parens.js
+++ b/src/language-js/needs-parens.js
@@ -216,9 +216,16 @@ function needsParens(path, options) {
     case "CallExpression": {
       let firstParentNotMemberExpression = parent;
       let i = 0;
+      // tagged templates are basically member expressions from a grammar perspective
+      // see https://tc39.github.io/ecma262/#prod-MemberExpression
+      // so are typescript's non-null assertions, though there's no grammar to point to
       while (
         firstParentNotMemberExpression &&
-        firstParentNotMemberExpression.type === "MemberExpression"
+        ((firstParentNotMemberExpression.type === "MemberExpression" &&
+          firstParentNotMemberExpression.object ===
+            path.getParentNode(i - 1)) ||
+          firstParentNotMemberExpression.type === "TaggedTemplateExpression" ||
+          firstParentNotMemberExpression.type === "TSNonNullExpression")
       ) {
         firstParentNotMemberExpression = path.getParentNode(++i);
       }
@@ -725,13 +732,6 @@ function needsParens(path, options) {
         return false;
       }
       return true;
-
-    case "TSNonNullExpression": {
-      return (
-        node.expression.type === "CallExpression" &&
-        parent.type === "NewExpression"
-      );
-    }
   }
 
   return false;
diff --git a/tests/new_expression/__snapshots__/jsfmt.spec.js.snap b/tests/new_expression/__snapshots__/jsfmt.spec.js.snap
index 971368b51..15e40b214 100644
--- a/tests/new_expression/__snapshots__/jsfmt.spec.js.snap
+++ b/tests/new_expression/__snapshots__/jsfmt.spec.js.snap
@@ -29,11 +29,17 @@ printWidth: 80
 new (memoize.Cache || MapCache)
 new (typeof this == "function" ? this : Dict())
 new (createObj()).prop(a());
+new (x()\`\`.y)();
+new e[f().x].y();
+new e[f()].y();
 
 =====================================output=====================================
 new (memoize.Cache || MapCache)();
 new (typeof this == "function" ? this : Dict())();
 new (createObj()).prop(a());
+new (x())\`\`.y();
+new e[f().x].y();
+new e[f()].y();
 
 ================================================================================
 `;
diff --git a/tests/new_expression/new_expression.js b/tests/new_expression/new_expression.js
index 144275d08..c85c355a8 100644
--- a/tests/new_expression/new_expression.js
+++ b/tests/new_expression/new_expression.js
@@ -1,3 +1,6 @@
 new (memoize.Cache || MapCache)
 new (typeof this == "function" ? this : Dict())
 new (createObj()).prop(a());
+new (x()``.y)();
+new e[f().x].y();
+new e[f()].y();
diff --git a/tests/typescript_non_null/__snapshots__/jsfmt.spec.js.snap b/tests/typescript_non_null/__snapshots__/jsfmt.spec.js.snap
index 62a40c40d..39235371d 100644
--- a/tests/typescript_non_null/__snapshots__/jsfmt.spec.js.snap
+++ b/tests/typescript_non_null/__snapshots__/jsfmt.spec.js.snap
@@ -62,6 +62,7 @@ const b = c!();
 // parens are necessary if the expression result is called as a constructor
 const c = new (d()!)();
 const c = new (d()!);
+const c = new (d()!.e)();
 
 =====================================output=====================================
 (a ? b : c)![tokenKey];
@@ -80,8 +81,9 @@ const a = b()!(); // parens aren't necessary
 const b = c!();
 
 // parens are necessary if the expression result is called as a constructor
-const c = new (d()!)();
-const c = new (d()!)();
+const c = new (d())!();
+const c = new (d())!();
+const c = new (d())!.e();
 
 ================================================================================
 `;
diff --git a/tests/typescript_non_null/parens.ts b/tests/typescript_non_null/parens.ts
index b6d1721ec..b96c63dda 100644
--- a/tests/typescript_non_null/parens.ts
+++ b/tests/typescript_non_null/parens.ts
@@ -16,3 +16,4 @@ const b = c!();
 // parens are necessary if the expression result is called as a constructor
 const c = new (d()!)();
 const c = new (d()!);
+const c = new (d()!.e)();