diff --git a/packages/babel-parser/src/plugins/flow.js b/packages/babel-parser/src/plugins/flow.js
index 59dd4de0c3..8dcbdf7a54 100644
--- a/packages/babel-parser/src/plugins/flow.js
+++ b/packages/babel-parser/src/plugins/flow.js
@@ -1935,7 +1935,9 @@ export default (superClass: Class<Parser>): Class<Parser> =>
     // ensure that inside flow types, we bypass the jsx parser plugin
     getTokenFromCode(code: number): void {
       const next = this.state.input.charCodeAt(this.state.pos + 1);
-      if (
+      if (code === charCodes.leftCurlyBrace && next === charCodes.verticalBar) {
+        return this.finishOp(tt.braceBarL, 2);
+      } else if (
         this.state.inType &&
         (code === charCodes.greaterThan || code === charCodes.lessThan)
       ) {
@@ -2701,6 +2703,20 @@ export default (superClass: Class<Parser>): Class<Parser> =>
       super.readToken_mult_modulo(code);
     }
 
+    readToken_pipe_amp(code: number): void {
+      const next = this.state.input.charCodeAt(this.state.pos + 1);
+      if (
+        code === charCodes.verticalBar &&
+        next === charCodes.rightCurlyBrace
+      ) {
+        // '|}'
+        this.finishOp(tt.braceBarR, 2);
+        return;
+      }
+
+      super.readToken_pipe_amp(code);
+    }
+
     parseTopLevel(file: N.File, program: N.Program): N.File {
       const fileNode = super.parseTopLevel(file, program);
       if (this.state.hasFlowComment) {
diff --git a/packages/babel-parser/src/tokenizer/index.js b/packages/babel-parser/src/tokenizer/index.js
index 038d58948e..4b5a7adc49 100644
--- a/packages/babel-parser/src/tokenizer/index.js
+++ b/packages/babel-parser/src/tokenizer/index.js
@@ -482,7 +482,7 @@ export default class Tokenizer extends LocationParser {
   }
 
   readToken_pipe_amp(code: number): void {
-    // '|&'
+    // '||' '&&' '||=' '&&='
     const next = this.state.input.charCodeAt(this.state.pos + 1);
 
     if (next === code) {
@@ -504,10 +504,6 @@ export default class Tokenizer extends LocationParser {
       if (next === charCodes.greaterThan) {
         this.finishOp(tt.pipeline, 2);
         return;
-      } else if (next === charCodes.rightCurlyBrace && this.hasPlugin("flow")) {
-        // '|}'
-        this.finishOp(tt.braceBarR, 2);
-        return;
       }
     }
 
@@ -688,20 +684,10 @@ export default class Tokenizer extends LocationParser {
         ++this.state.pos;
         this.finishToken(tt.bracketR);
         return;
-
       case charCodes.leftCurlyBrace:
-        if (
-          this.hasPlugin("flow") &&
-          this.state.input.charCodeAt(this.state.pos + 1) ===
-            charCodes.verticalBar
-        ) {
-          this.finishOp(tt.braceBarL, 2);
-        } else {
-          ++this.state.pos;
-          this.finishToken(tt.braceL);
-        }
+        ++this.state.pos;
+        this.finishToken(tt.braceL);
         return;
-
       case charCodes.rightCurlyBrace:
         ++this.state.pos;
         this.finishToken(tt.braceR);