diff --git a/examples/general/src/app/page.jsx b/examples/general/src/app/page.jsx
index 4b51e57..459db49 100644
--- a/examples/general/src/app/page.jsx
+++ b/examples/general/src/app/page.jsx
@@ -1,4 +1,5 @@
 import { Comp } from "./Comp";
+import { Comp as Comp2 } from "./Comp";
 
 export const dynamic = 'force-dynamic';
 
@@ -6,15 +7,22 @@ export default async function Page() {
   // throw new Error("This is a Page error");
 
   function renderTest() {
-    throw new Error("This is a render method error");
-    // return <span>Should not be wrapped</span>
+    // throw new Error("This is a render method error");
+    return <span>Should not be wrapped</span>
+  }
+
+  function ABC() {
+    // throw new Error("This is a ABC error");
+    return <div>ABC</div>
   }
 
   return (
     <div>
       <h1>Page</h1>
       <Comp />
+      <Comp2 />
       {renderTest()}
+      <ABC />
     </div>
   );
 }
diff --git a/packages/next-rsc-error-handler/src/index.d.ts b/packages/next-rsc-error-handler/src/index.d.ts
index 3833acc..1b59daa 100644
--- a/packages/next-rsc-error-handler/src/index.d.ts
+++ b/packages/next-rsc-error-handler/src/index.d.ts
@@ -1,6 +1,8 @@
 import { NextConfig } from "next";
 
-export interface RscErrorHandlerOptions {}
+export interface RscErrorHandlerOptions {
+  componentName: RegExp;
+}
 
 export function rscErrorHandler(
   options: RscErrorHandlerOptions
@@ -8,8 +10,7 @@ export function rscErrorHandler(
 
 export interface GlobalServerErrorContext {
   filePath: string;
-  functionName: string;
-  options: RscErrorHandlerOptions;
+  componentName: string;
 }
 
 export type GlobalServerError = (
diff --git a/packages/next-rsc-error-handler/src/index.js b/packages/next-rsc-error-handler/src/index.js
index 636f586..26365a8 100644
--- a/packages/next-rsc-error-handler/src/index.js
+++ b/packages/next-rsc-error-handler/src/index.js
@@ -1,4 +1,6 @@
-const defaultOptions = {};
+const defaultOptions = {
+  componentName: /^[A-Z]/,
+};
 
 export function rscErrorHandler(options = {}) {
   return function withLoader(nextConfig = {}) {
diff --git a/packages/next-rsc-error-handler/src/loader.js b/packages/next-rsc-error-handler/src/loader.js
index 4ae0b4f..71708ac 100644
--- a/packages/next-rsc-error-handler/src/loader.js
+++ b/packages/next-rsc-error-handler/src/loader.js
@@ -6,8 +6,9 @@ import * as t from "@babel/types";
 import {
   getRelativePath,
   isClientComponent,
-  isReactElement,
-  wrapWithFunction,
+  wrapFunctionDeclaration,
+  wrapArrowFunction,
+  getOptionsExpressionLiteral,
 } from "./utils.js";
 
 const WRAPPER_NAME = "__rscWrapper";
@@ -28,26 +29,31 @@ export default function (source) {
 
   let wasWrapped = false;
 
-  traverse.default(ast, {
-    enter(p) {
-      if (!p.isFunctionDeclaration() && !p.isArrowFunctionExpression()) {
-        return;
-      }
+  function wrapIfComponent(functionName, p, wrapFn) {
+    if (!options.componentName.test(functionName)) {
+      return;
+    }
 
-      if (!isReactElement(p)) {
-        return;
-      }
+    const ctx = {
+      filePath: getRelativePath(resourcePath),
+      componentName: functionName,
+    };
+    const optionsExpression = getOptionsExpressionLiteral(ctx);
 
-      const ctx = {
-        filePath: getRelativePath(resourcePath),
-        functionName: getFunctionName(p),
-        options,
-      };
+    wasWrapped = true;
 
-      wasWrapped = true;
-      wrapWithFunction(p, WRAPPER_NAME, ctx);
+    wrapFn(p, WRAPPER_NAME, optionsExpression);
+  }
 
-      p.skip();
+  traverse.default(ast, {
+    // TODO add FunctionExpression
+    FunctionDeclaration(p) {
+      const functionName = p.node.id?.name ?? "";
+      wrapIfComponent(functionName, p, wrapFunctionDeclaration);
+    },
+    ArrowFunctionExpression(p) {
+      const functionName = getArrowFunctionName(p);
+      wrapIfComponent(functionName, p, wrapArrowFunction);
     },
   });
 
@@ -59,19 +65,14 @@ export default function (source) {
   return output.code;
 }
 
-function getFunctionName(p) {
-  if (p.isFunctionDeclaration()) {
-    return p.node.id?.name;
-  }
-
+function getArrowFunctionName(p) {
   if (p.isArrowFunctionExpression()) {
     const parent = p.parentPath;
     if (parent.isVariableDeclarator() && parent.node.id.type === "Identifier") {
       return parent.node.id.name;
     }
   }
-
-  return "(anonymous)";
+  return "";
 }
 
 function addImport(ast) {
diff --git a/packages/next-rsc-error-handler/src/utils.js b/packages/next-rsc-error-handler/src/utils.js
index 019ddf0..42ec8be 100644
--- a/packages/next-rsc-error-handler/src/utils.js
+++ b/packages/next-rsc-error-handler/src/utils.js
@@ -10,64 +10,6 @@ export function isClientComponent(source) {
   return source.includes("__next_internal_client_entry_do_not_use__");
 }
 
-/**
- * Return true if node is a function and returns jsx.
- * @param {Path} p
- * @returns {boolean}
- */
-export function isReactElement(p) {
-  let isReactElement = false;
-  if (p.isFunctionDeclaration() || p.isArrowFunctionExpression()) {
-    isReactElement = isReturningJSXElement(p);
-  }
-
-  return isReactElement;
-}
-
-const JSX_FN_NAMES =
-  process.env.NODE_ENV === "production"
-    ? ["_jsx", "_jsxs"]
-    : ["_jsxDEV", "_jsxsDEV"];
-
-/**
- * Helper function that returns true if node returns a JSX element.
- * @param {Path} p
- * @returns {boolean}
- */
-function isReturningJSXElement(p) {
-  let foundJSX = false;
-
-  p.traverse({
-    CallExpression(innerP) {
-      const calleePath = innerP.get("callee");
-      if (
-        t.isIdentifier(calleePath.node) &&
-        JSX_FN_NAMES.includes(calleePath.node.name)
-      ) {
-        foundJSX = true;
-        innerP.stop();
-      }
-    },
-  });
-
-  return foundJSX;
-}
-
-/**
- * Wraps FunctionDeclaration or ArrowFunctionExpression with a function call with context.
- */
-export function wrapWithFunction(p, wrapFunctionName, context) {
-  const optionsExpression = getOptionsExpressionLiteral(context);
-
-  if (p.isArrowFunctionExpression()) {
-    return wrapArrowFunction(p, wrapFunctionName, optionsExpression);
-  } else if (p.isFunctionDeclaration()) {
-    return wrapFunctionDeclaration(p, wrapFunctionName, optionsExpression);
-  } else {
-    throw new Error("Unsupported type of function");
-  }
-}
-
 function getOptionsExpression(obj) {
   return t.objectExpression(
     Object.entries(obj).map(([key, value]) =>
@@ -76,7 +18,7 @@ function getOptionsExpression(obj) {
   );
 }
 
-function getOptionsExpressionLiteral(value) {
+export function getOptionsExpressionLiteral(value) {
   if (value === null) {
     return t.nullLiteral();
   }
@@ -96,13 +38,17 @@ function getOptionsExpressionLiteral(value) {
   }
 }
 
-function wrapArrowFunction(p, wrapFunctionName, optionsNode) {
+export function wrapArrowFunction(p, wrapFunctionName, optionsNode) {
   return p.replaceWith(
     t.callExpression(t.identifier(wrapFunctionName), [p.node, optionsNode])
   );
 }
 
-function wrapFunctionDeclaration(p, wrapFunctionName, argumentsExpression) {
+export function wrapFunctionDeclaration(
+  p,
+  wrapFunctionName,
+  argumentsExpression
+) {
   const expression = t.functionExpression(
     null,
     p.node.params,
@@ -112,8 +58,7 @@ function wrapFunctionDeclaration(p, wrapFunctionName, argumentsExpression) {
   );
 
   if (p.node.id == null) {
-    // FIXME should work no matter if there is no function name
-    throw new Error("FunctionDeclaration has no id.");
+    throw new Error("FunctionDeclaration has no name");
   }
 
   const originalFunctionIdentifier = t.identifier(p.node.id.name);