diff --git a/input_files.cc b/input_files.cc
index 87786194..1ab64ded 100644
--- a/input_files.cc
+++ b/input_files.cc
@@ -60,9 +60,9 @@ void ObjectFile::initialize_sections() {
       if (entries[0] != GRP_COMDAT)
         error(toString(this) + ": unsupported SHT_GROUP format");
 
-      static ConcurrentMap<bool> map;
-      bool *handle = map.insert(signature, false);
-      comdat_groups.push_back({handle, entries});
+      static ConcurrentMap<ComdatGroup> map;
+      ComdatGroup *group = map.insert(signature, ComdatGroup(this, i));
+      comdat_groups.push_back({group, i});
       num_comdats++;
       break;
     }
@@ -120,6 +120,14 @@ void ObjectFile::initialize_symbols() {
   }
 }
 
+void ObjectFile::remove_comdat_members(uint32_t section_idx) {
+  const ELF64LE::Shdr &shdr = elf_sections[section_idx];
+  ArrayRef<ELF64LE::Word> entries =
+    CHECK(obj.template getSectionContentsAsArray<ELF64LE::Word>(shdr), this);
+  for (uint32_t i : entries)
+    sections[i] = nullptr;
+}
+
 void ObjectFile::read_string_pieces(const ELF64LE::Shdr &shdr) {
   static ConcurrentMap<StringPiece> map1;
   static ConcurrentMap<StringPiece> map2;
@@ -208,17 +216,28 @@ void ObjectFile::register_undefined_symbols() {
 }
 
 void ObjectFile::eliminate_duplicate_comdat_groups() {
-  for (std::pair<bool *, ArrayRef<ELF64LE::Word>> pair : comdat_groups) {
-    bool *handle = pair.first;
-    ArrayRef<ELF64LE::Word> entries = pair.second;
+  for (auto &pair : comdat_groups) {
+    ComdatGroup *g = pair.first;
+    uint32_t section_idx = pair.second;
 
-    if (!*handle) {
-      *handle = true;
-      continue;
+    ObjectFile *file = nullptr;
+    uint32_t idx = 0;
+
+    while (g->lock.test_and_set(std::memory_order_acquire));
+    if (g->file == nullptr) {
+      g->file = this;
+      g->section_idx = section_idx;
+    } else if (g->file->priority < this->priority) {
+      file = this;
+      idx = section_idx;
+    } else {
+      file = g->file;
+      idx = g->section_idx;
     }
-    
-    for (uint32_t i : entries)
-      sections[i] = nullptr;
+    g->lock.clear(std::memory_order_release);
+
+    if (file)
+      file->remove_comdat_members(idx);
   }
 }
 
diff --git a/main.cc b/main.cc
index 7049d595..add8dbf0 100644
--- a/main.cc
+++ b/main.cc
@@ -224,8 +224,7 @@ int main(int argc, char **argv) {
 
   // Eliminate duplicate comdat groups.
   comdat_timer.startTimer();
-  for (ObjectFile *file : files)
-    file->eliminate_duplicate_comdat_groups();
+  for_each(files, [](ObjectFile *file) { file->eliminate_duplicate_comdat_groups(); });
   comdat_timer.stopTimer();
 
   // Bin input sections into output sections
diff --git a/mold.h b/mold.h
index 73ef9ff4..dc596976 100644
--- a/mold.h
+++ b/mold.h
@@ -349,10 +349,21 @@ extern StringTableSection *shstrtab;
 // input_files.cc
 //
 
-class StringPiece {
-public:
+struct ComdatGroup {
+  ComdatGroup(ObjectFile *file, uint32_t i)
+    : file(file), section_idx(i) {}
+  ComdatGroup(const ComdatGroup &other)
+    : file(other.file), section_idx(other.section_idx) {}
+
+  std::atomic_flag lock = ATOMIC_FLAG_INIT;
+  ObjectFile *file = nullptr;
+  uint32_t section_idx;
+};
+
+struct StringPiece {
   StringPiece(StringRef data) : data(data) {}
   StringPiece(const StringPiece &other) : data(other.data) {}
+
   StringRef data;
   std::atomic_flag flag = ATOMIC_FLAG_INIT;
 };
@@ -377,11 +388,12 @@ public:
 private:
   void initialize_sections();
   void initialize_symbols();
+  void remove_comdat_members(uint32_t section_idx);
   void read_string_pieces(const ELF64LE::Shdr &shdr);
 
   MemoryBufferRef mb;
   std::vector<Symbol *> symbols;
-  std::vector<std::pair<bool *, ArrayRef<ELF64LE::Word>>> comdat_groups;
+  std::vector<std::pair<ComdatGroup *, uint32_t>> comdat_groups;
   std::vector<StringPiece *> merged_strings_alloc;
   std::vector<StringPiece *> merged_strings_noalloc;