diff --git a/acorn/src/expression.js b/acorn/src/expression.js
index 32d92d9ae..0d1b3fa8a 100644
--- a/acorn/src/expression.js
+++ b/acorn/src/expression.js
@@ -221,7 +221,7 @@ pp.buildBinary = function(startPos, startLoc, left, right, op, logical) {
 
 // Parse unary operators, both prefix and postfix.
 
-pp.parseMaybeUnary = function(refDestructuringErrors, sawUnary) {
+pp.parseMaybeUnary = function(refDestructuringErrors, sawUnary, incDec) {
   let startPos = this.start, startLoc = this.startLoc, expr
   if (this.isContextual("await") && (this.inAsync || (!this.inFunction && this.options.allowAwaitOutsideFunction))) {
     expr = this.parseAwait()
@@ -231,7 +231,7 @@ pp.parseMaybeUnary = function(refDestructuringErrors, sawUnary) {
     node.operator = this.value
     node.prefix = true
     this.next()
-    node.argument = this.parseMaybeUnary(null, true)
+    node.argument = this.parseMaybeUnary(null, true, update)
     this.checkExpressionErrors(refDestructuringErrors, true)
     if (update) this.checkLValSimple(node.argument)
     else if (this.strict && node.operator === "delete" &&
@@ -255,10 +255,14 @@ pp.parseMaybeUnary = function(refDestructuringErrors, sawUnary) {
     }
   }
 
-  if (!sawUnary && this.eat(tt.starstar))
-    return this.buildBinary(startPos, startLoc, expr, this.parseMaybeUnary(null, false), "**", false)
-  else
+  if (!incDec && this.eat(tt.starstar)) {
+    if (sawUnary)
+      this.unexpected(this.lastTokStart)
+    else
+      return this.buildBinary(startPos, startLoc, expr, this.parseMaybeUnary(null, false), "**", false)
+  } else {
     return expr
+  }
 }
 
 function isPrivateFieldAccess(node) {
diff --git a/test/tests-asyncawait.js b/test/tests-asyncawait.js
index e5ed2e7c5..7b0f4107c 100644
--- a/test/tests-asyncawait.js
+++ b/test/tests-asyncawait.js
@@ -3526,4 +3526,16 @@ testFail("abc: async function a() {}", "Unexpected token (1:5)", {ecmaVersion: 8
 
 testFail("(async() => { await 4 ** 2 })()", "Unexpected token (1:22)", {ecmaVersion: 8})
 
+test("(async() => { await (4 ** 2) })()", {}, {ecmaVersion: 8})
+
+testFail("async() => (await 1 ** 3)", "Unexpected token (1:20)", {ecmaVersion: 8})
+
+test("async() => (await (1 ** 3))", {}, {ecmaVersion: 8})
+
+testFail("async() => await 5 ** 6", "Unexpected token (1:19)", {ecmaVersion: 8})
+
+test("async() => await (5 ** 6)", {}, {ecmaVersion: 8})
+
+testFail("async() => await (5) ** 6", "Unexpected token (1:21)", {ecmaVersion: 8})
+
 testFail("4 + async() => 2", "Unexpected token (1:12)", {ecmaVersion: 8, loose: false})
diff --git a/test/tests-es7.js b/test/tests-es7.js
index 4130cb22d..b5c251ce3 100644
--- a/test/tests-es7.js
+++ b/test/tests-es7.js
@@ -228,6 +228,8 @@ testFail("~3 ** 2;", "Unexpected token (1:3)", { ecmaVersion: 7 });
 testFail("!1 ** 2;", "Unexpected token (1:3)", { ecmaVersion: 7 });
 testFail("-2** 2;", "Unexpected token (1:2)", { ecmaVersion: 7 });
 testFail("+2** 2;", "Unexpected token (1:2)", { ecmaVersion: 7 });
+testFail("-(i--) ** 2", "Unexpected token (1:7)", {ecmaVersion: 7});
+testFail("+(i--) ** 2", "Unexpected token (1:7)", {ecmaVersion: 7});
 
 // make sure base operand check doesn't affect other operators
 test("-a * 5", {