diff --git a/MdePkg/Library/PeiMemoryAllocationLib/MemoryAllocationLib.c b/MdePkg/Library/PeiMemoryAllocationLib/MemoryAllocationLib.c
index a240d03ef3..f9e723ef2f 100644
--- a/MdePkg/Library/PeiMemoryAllocationLib/MemoryAllocationLib.c
+++ b/MdePkg/Library/PeiMemoryAllocationLib/MemoryAllocationLib.c
@@ -644,8 +644,8 @@ AllocateReservedCopyPool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
   
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  PoolType       The type of pool to allocate.
   @param  OldSize        The size, in bytes, of OldBuffer.
@@ -666,7 +666,7 @@ InternalReallocatePool (
 {
   VOID  *NewBuffer;
 
-  NewBuffer = AllocateZeroPool (NewSize);
+  NewBuffer = InternalAllocateZeroPool (PoolType, NewSize);
   if (NewBuffer != NULL && OldBuffer != NULL) {
     CopyMem (NewBuffer, OldBuffer, MIN (OldSize, NewSize));
     FreePool (OldBuffer);
@@ -684,8 +684,8 @@ InternalReallocatePool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
   
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  OldSize        The size, in bytes, of OldBuffer.
   @param  NewSize        The size, in bytes, of the buffer to reallocate.
@@ -716,8 +716,8 @@ ReallocatePool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
 
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  OldSize        The size, in bytes, of OldBuffer.
   @param  NewSize        The size, in bytes, of the buffer to reallocate.
@@ -748,8 +748,8 @@ ReallocateRuntimePool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
 
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  OldSize        The size, in bytes, of OldBuffer.
   @param  NewSize        The size, in bytes, of the buffer to reallocate.
diff --git a/MdePkg/Library/UefiMemoryAllocationLib/MemoryAllocationLib.c b/MdePkg/Library/UefiMemoryAllocationLib/MemoryAllocationLib.c
index 1cf829babb..2a9f128424 100644
--- a/MdePkg/Library/UefiMemoryAllocationLib/MemoryAllocationLib.c
+++ b/MdePkg/Library/UefiMemoryAllocationLib/MemoryAllocationLib.c
@@ -661,8 +661,8 @@ AllocateReservedCopyPool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
   
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  PoolType       The type of pool to allocate.
   @param  OldSize        The size, in bytes, of OldBuffer.
@@ -701,8 +701,8 @@ InternalReallocatePool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
   
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  OldSize        The size, in bytes, of OldBuffer.
   @param  NewSize        The size, in bytes, of the buffer to reallocate.
@@ -733,8 +733,8 @@ ReallocatePool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
 
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  OldSize        The size, in bytes, of OldBuffer.
   @param  NewSize        The size, in bytes, of the buffer to reallocate.
@@ -765,8 +765,8 @@ ReallocateRuntimePool (
   If NewSize is 0, then a valid buffer of 0 size is  returned.  If there is not 
   enough memory remaining to satisfy the request, then NULL is returned.
 
-  If NewSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
-  If OldSize is greater than (MAX_ADDRESS - Buffer + 1), then ASSERT(). 
+  If the smaller of NewSize and OldSize is greater than (MAX_ADDRESS - OldBuffer + 1),
+  then ASSERT(). 
 
   @param  OldSize        The size, in bytes, of OldBuffer.
   @param  NewSize        The size, in bytes, of the buffer to reallocate.