diff --git a/main.cc b/main.cc
index 17a030fc..6399f814 100644
--- a/main.cc
+++ b/main.cc
@@ -140,6 +140,16 @@ static std::vector<ArrayRef<T>> split(const std::vector<T> &input, int unit) {
   return vec;
 }
 
+static void eliminate_comdats(std::vector<ObjectFile *> &files) {
+  tbb::parallel_for_each(files, [](ObjectFile *file) {
+    file->resolve_comdat_groups();
+  });
+
+  tbb::parallel_for_each(files, [](ObjectFile *file) {
+    file->eliminate_duplicate_comdat_groups();
+  });
+}
+
 static void handle_mergeable_strings(std::vector<ObjectFile *> &files) {
   // Resolve mergeable string pieces
   tbb::parallel_for_each(files, [](ObjectFile *file) {
@@ -778,9 +788,7 @@ int main(int argc, char **argv) {
   // Eliminate duplicate comdat groups.
   {
     MyTimer t("comdat", before_copy);
-    tbb::parallel_for_each(files, [](ObjectFile *file) {
-      file->eliminate_duplicate_comdat_groups();
-    });
+    eliminate_comdats(files);
   }
 
   // Resolve mergeable strings
diff --git a/mold.h b/mold.h
index 1cf298f0..525a8c11 100644
--- a/mold.h
+++ b/mold.h
@@ -557,7 +557,6 @@ struct ComdatGroup {
   ComdatGroup(const ComdatGroup &other)
     : file(other.file.load()), section_idx(other.section_idx) {}
 
-  tbb::spin_mutex mu;
   std::atomic<ObjectFile *> file;
   u32 section_idx;
 };
@@ -571,6 +570,7 @@ public:
   void resolve_symbols();
   void mark_live_archive_members(tbb::parallel_do_feeder<ObjectFile *> &feeder);
   void hanlde_undefined_weak_symbols();
+  void resolve_comdat_groups();
   void eliminate_duplicate_comdat_groups();
   void assign_mergeable_string_offsets();
   void convert_common_symbols();
diff --git a/object_file.cc b/object_file.cc
index a6148fa5..3cfe0716 100644
--- a/object_file.cc
+++ b/object_file.cc
@@ -408,40 +408,22 @@ void ObjectFile::hanlde_undefined_weak_symbols() {
   }
 }
 
+void ObjectFile::resolve_comdat_groups() {
+  for (auto &pair : comdat_groups) {
+    ComdatGroup *group = pair.first;
+    ObjectFile *cur = group->file;
+    while (!cur || cur->priority > this->priority)
+      if (group->file.compare_exchange_strong(cur, this))
+        break;
+  }
+}
+
 void ObjectFile::eliminate_duplicate_comdat_groups() {
   for (auto &pair : comdat_groups) {
-    ComdatGroup *g = pair.first;
+    ComdatGroup *group = pair.first;
     u32 section_idx = pair.second;
-
-    ObjectFile *other = g->file;
-    if (other && other->priority < this->priority) {
-      this->remove_comdat_members(section_idx);
-      continue;
-    }
-
-    ObjectFile *file;
-    u32 idx;
-
-    {
-      std::lock_guard lock(g->mu);
-      if (g->file == nullptr) {
-        g->file = this;
-        g->section_idx = section_idx;
-        continue;
-      }
-
-      if (g->file.load()->priority < this->priority) {
-        file = this;
-        idx = section_idx;
-      } else {
-        file = g->file;
-        idx = g->section_idx;
-        g->file = this;
-        g->section_idx = section_idx;
-      }
-    }
-
-    file->remove_comdat_members(idx);
+    if (group->file != this)
+      remove_comdat_members(section_idx);
   }
 }