diff --git a/be/src/exprs/aggregate-functions-ir.cc b/be/src/exprs/aggregate-functions-ir.cc
index 79d7ac791..853661c4f 100644
--- a/be/src/exprs/aggregate-functions-ir.cc
+++ b/be/src/exprs/aggregate-functions-ir.cc
@@ -1388,6 +1388,7 @@ void AggregateFunctions::LastValUpdate(FunctionContext* ctx, const StringVal& sr
   } else {
     new_ptr = ctx->Reallocate(dst->ptr, src.len);
   }
+  // Note that a zero-length string is not the same as StringVal::null().
   RETURN_IF_NULL(ctx, new_ptr);
   dst->ptr = new_ptr;
   memcpy(dst->ptr, src.ptr, src.len);
diff --git a/be/src/runtime/free-pool.h b/be/src/runtime/free-pool.h
index 90df74992..8762f1df2 100644
--- a/be/src/runtime/free-pool.h
+++ b/be/src/runtime/free-pool.h
@@ -62,12 +62,10 @@ class FreePool {
       return NULL;
     }
 #endif
-    ++net_allocations_;
-    if (FLAGS_disable_mem_pools) return reinterpret_cast<uint8_t*>(malloc(size));
-
     /// Return a non-NULL dummy pointer. NULL is reserved for failures.
     if (UNLIKELY(size == 0)) return mem_pool_->EmptyAllocPtr();
-
+    ++net_allocations_;
+    if (FLAGS_disable_mem_pools) return reinterpret_cast<uint8_t*>(malloc(size));
     int free_list_idx = Bits::Log2Ceiling64(size);
     DCHECK_LT(free_list_idx, NUM_LISTS);
     FreeListNode* allocation = lists_[free_list_idx].next;
@@ -92,12 +90,12 @@ class FreePool {
   }
 
   void Free(uint8_t* ptr) {
+    if (UNLIKELY(ptr == NULL || ptr == mem_pool_->EmptyAllocPtr())) return;
     --net_allocations_;
     if (FLAGS_disable_mem_pools) {
       free(ptr);
       return;
     }
-    if (UNLIKELY(ptr == NULL || ptr == mem_pool_->EmptyAllocPtr())) return;
     FreeListNode* node = reinterpret_cast<FreeListNode*>(ptr - sizeof(FreeListNode));
     FreeListNode* list = node->list;
 #ifndef NDEBUG
diff --git a/be/src/udf/udf-test.cc b/be/src/udf/udf-test.cc
index 4857a0630..86f02c2cb 100644
--- a/be/src/udf/udf-test.cc
+++ b/be/src/udf/udf-test.cc
@@ -123,8 +123,9 @@ IntVal ValidateFail(FunctionContext* context) {
 }
 
 IntVal ValidateMem(FunctionContext* context) {
-  EXPECT_TRUE(context->Allocate(0) == NULL);
-  uint8_t* buffer = context->Allocate(10);
+  uint8_t* buffer = context->Allocate(0);
+  EXPECT_TRUE(buffer != NULL);
+  buffer = context->Reallocate(buffer, 10);
   EXPECT_TRUE(buffer != NULL);
   memset(buffer, 0, 10);
   context->Free(buffer);
diff --git a/be/src/udf/udf.cc b/be/src/udf/udf.cc
index ff81c9c04..c1fb5be42 100644
--- a/be/src/udf/udf.cc
+++ b/be/src/udf/udf.cc
@@ -286,7 +286,6 @@ inline bool FunctionContextImpl::CheckAllocResult(const char* fn_name,
 
 uint8_t* FunctionContext::Allocate(int byte_size) noexcept {
   assert(!impl_->closed_);
-  if (byte_size == 0) return NULL;
   uint8_t* buffer = impl_->pool_->Allocate(byte_size);
   if (UNLIKELY(!impl_->CheckAllocResult("FunctionContext::Allocate",
       buffer, byte_size))) {
@@ -418,7 +417,6 @@ void FunctionContext::SetFunctionState(FunctionStateScope scope, void* ptr) {
 
 uint8_t* FunctionContextImpl::AllocateLocal(int64_t byte_size) noexcept {
   assert(!closed_);
-  if (byte_size == 0) return NULL;
   uint8_t* buffer = pool_->Allocate(byte_size);
   if (UNLIKELY(!CheckAllocResult("FunctionContextImpl::AllocateLocal",
       buffer, byte_size))) {
diff --git a/testdata/workloads/functional-query/queries/QueryTest/aggregation.test b/testdata/workloads/functional-query/queries/QueryTest/aggregation.test
index 5389b04f3..740f777a6 100644
--- a/testdata/workloads/functional-query/queries/QueryTest/aggregation.test
+++ b/testdata/workloads/functional-query/queries/QueryTest/aggregation.test
@@ -154,13 +154,31 @@ from alltypesagg where day is not null
 bigint, string, string, string, string
 ====
 ---- QUERY
-# Test for IMPALA-3018. Verify update() function of min() handles
+# Test for IMPALA-3018. Verify update() functions of min() and max() handle
 # zero-length string correctly.
-select min(str) from (values ('aaa' as str), ('')) as tmp
+select max(str), min(str) from (values ('aaa' as str), (''), ('123')) as tmp
+---- RESULTS
+'aaa',''
+---- TYPES
+string,string
+====
+---- QUERY
+# Test for IMPALA-3018. Verify update() function of last_value() handles
+# zero-length string correctly.
+select last_value(b) over (partition by a order by d) from functional.nulltable;
 ---- RESULTS
 ''
 ---- TYPES
-String
+string
+====
+---- QUERY
+# Test for IMPALA-3018. Verify update() function of first_value() handles
+# zero-length string correctly.
+select first_value(b) over (partition by a order by d) from functional.nulltable;
+---- RESULTS
+''
+---- TYPES
+string
 ====
 ---- QUERY
 # grouping by different data types, with NULLs