diff --git a/packages/babel-parser/src/parser/statement.js b/packages/babel-parser/src/parser/statement.js
index 1f895ee973f9..0f6ce71dcf31 100644
--- a/packages/babel-parser/src/parser/statement.js
+++ b/packages/babel-parser/src/parser/statement.js
@@ -1442,11 +1442,9 @@ export default class StatementParser extends ExpressionParser {
       return;
     }
 
-    const containsEsc = this.state.containsEsc;
+    const isContextual = this.match(tt.name) && !this.state.containsEsc;
     const isPrivate = this.match(tt.privateName);
     const key = this.parseClassElementName(member);
-    // Check the key is not a computed expression or string literal.
-    const isSimple = key.type === "Identifier";
     const maybeQuestionTokenStart = this.state.start;
 
     this.parsePostMemberNameModifiers(publicMember);
@@ -1491,9 +1489,8 @@ export default class StatementParser extends ExpressionParser {
         this.pushClassProperty(classBody, publicProp);
       }
     } else if (
-      isSimple &&
+      isContextual &&
       key.name === "async" &&
-      !containsEsc &&
       !this.isLineTerminator()
     ) {
       // an async method
@@ -1532,9 +1529,8 @@ export default class StatementParser extends ExpressionParser {
         );
       }
     } else if (
-      isSimple &&
+      isContextual &&
       (key.name === "get" || key.name === "set") &&
-      !containsEsc &&
       !(this.match(tt.star) && this.isLineTerminator())
     ) {
       // `get\n*` is an uninitialized property named 'get' followed by a generator.
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-identifier/input.js b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-identifier/input.js
new file mode 100644
index 000000000000..b565a2946faa
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-identifier/input.js
@@ -0,0 +1,3 @@
+class A {
+  [async] a() {}
+}
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-identifier/options.json b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-identifier/options.json
new file mode 100644
index 000000000000..239667c16b9e
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-identifier/options.json
@@ -0,0 +1,3 @@
+{
+  "throws": "Unexpected token (2:10)"
+}
\ No newline at end of file
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async/input.js b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-string/input.js
similarity index 100%
rename from packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async/input.js
rename to packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-string/input.js
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async/options.json b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-string/options.json
similarity index 100%
rename from packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async/options.json
rename to packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-async-string/options.json
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-identifier/input.js b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-identifier/input.js
new file mode 100644
index 000000000000..c9bd13ebefd0
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-identifier/input.js
@@ -0,0 +1,3 @@
+class A {
+  [get] a() {}
+}
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-identifier/options.json b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-identifier/options.json
new file mode 100644
index 000000000000..c7c23f0899e3
--- /dev/null
+++ b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-identifier/options.json
@@ -0,0 +1,3 @@
+{
+  "throws": "Unexpected token (2:8)"
+}
\ No newline at end of file
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get/input.js b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-string/input.js
similarity index 100%
rename from packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get/input.js
rename to packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-string/input.js
diff --git a/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get/options.json b/packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-string/options.json
similarity index 100%
rename from packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get/options.json
rename to packages/babel-parser/test/fixtures/es2015/class-methods/disallow-computed-get-string/options.json