diff --git a/libcxxabi/src/demangle/Utility.h b/libcxxabi/src/demangle/Utility.h
--- a/libcxxabi/src/demangle/Utility.h
+++ b/libcxxabi/src/demangle/Utility.h
@@ -37,10 +37,10 @@
   void grow(size_t N) {
     size_t Need = N + CurrentPosition;
     if (Need > BufferCapacity) {
-      // Avoid many reallocations during startup, with a bit of hysteresis.
-      constexpr size_t MinInitAlloc = 1024;
-      if (Need < MinInitAlloc)
-        Need = MinInitAlloc;
+      // Reduce the number of reallocations, with a bit of hysteresis. The
+      // number here is chosen so the first allocation will more-than-likely not
+      // allocate more than 1K.
+      Need += 1024 - 32;
       BufferCapacity *= 2;
       if (BufferCapacity < Need)
         BufferCapacity = Need;
diff --git a/llvm/include/llvm/Demangle/Utility.h b/llvm/include/llvm/Demangle/Utility.h
--- a/llvm/include/llvm/Demangle/Utility.h
+++ b/llvm/include/llvm/Demangle/Utility.h
@@ -37,10 +37,10 @@
   void grow(size_t N) {
     size_t Need = N + CurrentPosition;
     if (Need > BufferCapacity) {
-      // Avoid many reallocations during startup, with a bit of hysteresis.
-      constexpr size_t MinInitAlloc = 1024;
-      if (Need < MinInitAlloc)
-        Need = MinInitAlloc;
+      // Reduce the number of reallocations, with a bit of hysteresis. The
+      // number here is chosen so the first allocation will more-than-likely not
+      // allocate more than 1K.
+      Need += 1024 - 32;
       BufferCapacity *= 2;
       if (BufferCapacity < Need)
         BufferCapacity = Need;
diff --git a/llvm/unittests/Demangle/OutputBufferTest.cpp b/llvm/unittests/Demangle/OutputBufferTest.cpp
--- a/llvm/unittests/Demangle/OutputBufferTest.cpp
+++ b/llvm/unittests/Demangle/OutputBufferTest.cpp
@@ -78,3 +78,16 @@
 
   std::free(OB.getBuffer());
 }
+
+// Test when initial needed size is larger than the default.
+TEST(OutputBufferTest, Extend) {
+  OutputBuffer OB;
+
+  char Massive[2000];
+  std::memset(Massive, 'a', sizeof(Massive));
+  Massive[sizeof(Massive) - 1] = 0;
+  OB << Massive;
+  EXPECT_EQ(Massive, toString(OB));
+
+  std::free(OB.getBuffer());
+}