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
@@ -213,7 +213,7 @@
   // Align allocation size.
   size = RoundUpTo(size, low_level_alloc_min_alignment);
   if (allocated_end_ - allocated_current_ < (sptr)size) {
-    uptr size_to_allocate = Max(size, GetPageSizeCached());
+    uptr size_to_allocate = RoundUpTo(size, GetPageSizeCached());
     allocated_current_ =
         (char*)MmapOrDie(size_to_allocate, __func__);
     allocated_end_ = allocated_current_ + size_to_allocate;
diff --git a/compiler-rt/lib/sanitizer_common/tests/sanitizer_allocator_test.cpp b/compiler-rt/lib/sanitizer_common/tests/sanitizer_allocator_test.cpp
--- a/compiler-rt/lib/sanitizer_common/tests/sanitizer_allocator_test.cpp
+++ b/compiler-rt/lib/sanitizer_common/tests/sanitizer_allocator_test.cpp
@@ -1404,4 +1404,15 @@
   EXPECT_EQ((uptr)TestMapUnmapCallback::unmap_count, m.size1());
 }
 
+TEST(SanitizerCommon, LowLevelAllocatorShouldRoundUpSizeOnAlloc) {
+  // When allocating a memory block slightly bigger than a memory page and
+  // LowLevelAllocator calls MmapOrDie for the internal buffer, it should round
+  // the size up to the page size, so that subsequent calls to the allocator
+  // can use the remaining space in the last allocated page.
+  static LowLevelAllocator allocator;
+  char *ptr1 = (char *)allocator.Allocate(GetPageSizeCached() + 16);
+  char *ptr2 = (char *)allocator.Allocate(16);
+  EXPECT_EQ(ptr2, ptr1 + GetPageSizeCached() + 16);
+}
+
 #endif  // #if !SANITIZER_DEBUG