diff --git a/src/RPCServer.ts b/src/RPCServer.ts
index 4a75143..1b183d7 100644
--- a/src/RPCServer.ts
+++ b/src/RPCServer.ts
@@ -37,34 +37,36 @@ import * as events from './events';
 
 const cleanupReason = Symbol('CleanupReason');
 
-function composeMessage(error: unknown): string {
-  if (
-    typeof error === 'boolean' ||
-    typeof error === 'number' ||
-    typeof error === 'string' ||
-    typeof error === 'bigint' ||
-    typeof error === 'symbol'
-  ) {
-    return `Non-error literal ${String(error)} was thrown`;
-  }
-  if (
-    typeof error === 'object' &&
-    error != null &&
-    'message' in error &&
-    error.message != null
-  ) {
-    return String(error.message);
-  }
-  if (typeof error === 'object' && error?.constructor?.name != null) {
-    return `Non-error object ${error.constructor.name} was thrown`;
+function composeErrorMessage(error: unknown): string {
+  switch (typeof error) {
+    case 'boolean':
+    case 'number':
+    case 'string':
+    case 'bigint':
+    case 'symbol':
+      return `Non-error literal ${String(error)} was thrown`;
+    case 'object':
+      // Let the fallback handler catch null values.
+      if (error == null) break;
+      // If we have an error message defined, then return that.
+      if ('message' in error && typeof error.message === 'string') {
+        return error.message;
+      }
+      // If present, mention the constructor name in the message.
+      if (error.constructor?.name != null) {
+        return `Non-error object ${error.constructor.name} was thrown`;
+      }
+      // Any other values should be handled by the fallback handler.
+      break;
   }
-  // If an object is not serialisable (for example, Object.create(null)), then
-  // an error would be raised when trying to convert it to a string. In that
-  // case, simply avoid serialising the error.
+
+  // Handle cases where the error is not serialisable, like objects created
+  // using Object.create(null). Trying to serialise this throws a TypeError.
   try {
-    return `Non-error value ${error} was thrown`;
+    return `Non-error value ${String(error)} was thrown`;
   } catch (e) {
-    return 'Non-error value was thrown'
+    if (e instanceof TypeError) return 'Non-error value was thrown';
+    else throw e;
   }
 }
 
@@ -358,7 +360,7 @@ class RPCServer {
             try {
               const rpcError: JSONRPCResponseError = {
                 code: errors.JSONRPCResponseErrorCode.RPCRemote,
-                message: composeMessage(e),
+                message: composeErrorMessage(e),
                 data: this.fromError(e),
               };
               const rpcErrorMessage: JSONRPCResponseFailed = {
@@ -630,7 +632,7 @@ class RPCServer {
         try {
           const rpcError: JSONRPCResponseError = {
             code: errors.JSONRPCResponseErrorCode.RPCRemote,
-            message: composeMessage(e),
+            message: composeErrorMessage(e),
             data: this.fromError(e),
           };
           const rpcErrorMessage: JSONRPCResponseFailed = {