diff --git a/compiler-rt/lib/sanitizer_common/sanitizer_allocator.cpp b/compiler-rt/lib/sanitizer_common/sanitizer_allocator.cpp
--- a/compiler-rt/lib/sanitizer_common/sanitizer_allocator.cpp
+++ b/compiler-rt/lib/sanitizer_common/sanitizer_allocator.cpp
@@ -138,6 +138,8 @@
 
 // LowLevelAllocator
 constexpr uptr kLowLevelAllocatorDefaultAlignment = 8;
+constexpr uptr kMinNumPagesRounded = 16;
+constexpr uptr kMinRoundedSize = 65536;
 static uptr low_level_alloc_min_alignment = kLowLevelAllocatorDefaultAlignment;
 static LowLevelAllocateCallback low_level_alloc_callback;
 
@@ -145,7 +147,8 @@
   // Align allocation size.
   size = RoundUpTo(size, low_level_alloc_min_alignment);
   if (allocated_end_ - allocated_current_ < (sptr)size) {
-    uptr size_to_allocate = RoundUpTo(size, GetPageSizeCached());
+    uptr size_to_allocate = RoundUpTo(
+        size, Min(GetPageSizeCached() * kMinNumPagesRounded, kMinRoundedSize));
     allocated_current_ = (char *)MmapOrDie(size_to_allocate, __func__);
     allocated_end_ = allocated_current_ + size_to_allocate;
     if (low_level_alloc_callback) {