diff --git a/test/functional/rpc_blockchain.py b/test/functional/rpc_blockchain.py
index 98147237b10..5a91cab59e1 100755
--- a/test/functional/rpc_blockchain.py
+++ b/test/functional/rpc_blockchain.py
@@ -633,6 +633,19 @@ class BlockchainTest(BitcoinTestFramework):
         assert 'previousblockhash' not in node.getblock(node.getblockhash(0))
         assert 'nextblockhash' not in node.getblock(node.getbestblockhash())
 
+        self.log.info("Test getblock when only header is known")
+        current_height = node.getblock(node.getbestblockhash())['height']
+        block_time = node.getblock(node.getbestblockhash())['time'] + 1
+        block = create_block(int(blockhash, 16), create_coinbase(current_height + 1, nValue=100), block_time)
+        block.solve()
+        node.submitheader(block.serialize().hex())
+        assert_raises_rpc_error(-1, "Block not available (not fully downloaded)", lambda: node.getblock(block.hash))
+
+        self.log.info("Test getblock when block is missing")
+        move_block_file('blk00000.dat', 'blk00000.dat.bak')
+        assert_raises_rpc_error(-1, "Block not found on disk", node.getblock, blockhash)
+        move_block_file('blk00000.dat.bak', 'blk00000.dat')
+
 
 if __name__ == '__main__':
     BlockchainTest(__file__).main()
diff --git a/test/functional/rpc_getblockstats.py b/test/functional/rpc_getblockstats.py
index d1e4895eb6d..002763201a5 100755
--- a/test/functional/rpc_getblockstats.py
+++ b/test/functional/rpc_getblockstats.py
@@ -114,7 +114,7 @@ class GetblockstatsTest(BitcoinTestFramework):
         assert_equal(stats[self.max_stat_pos]['height'], self.start_height + self.max_stat_pos)
 
         for i in range(self.max_stat_pos+1):
-            self.log.info('Checking block %d\n' % (i))
+            self.log.info('Checking block %d' % (i))
             assert_equal(stats[i], self.expected_stats[i])
 
             # Check selecting block by hash too
@@ -182,5 +182,16 @@ class GetblockstatsTest(BitcoinTestFramework):
         assert_equal(tip_stats["utxo_increase_actual"], 4)
         assert_equal(tip_stats["utxo_size_inc_actual"], 300)
 
+        self.log.info("Test when only header is known")
+        block = self.generateblock(self.nodes[0], output="raw(55)", transactions=[], submit=False)
+        self.nodes[0].submitheader(block["hex"])
+        assert_raises_rpc_error(-1, "Block not available (not fully downloaded)", lambda: self.nodes[0].getblockstats(block['hash']))
+
+        self.log.info('Test when block is missing')
+        (self.nodes[0].blocks_path / 'blk00000.dat').rename(self.nodes[0].blocks_path / 'blk00000.dat.backup')
+        assert_raises_rpc_error(-1, 'Block not found on disk', self.nodes[0].getblockstats, hash_or_height=1)
+        (self.nodes[0].blocks_path / 'blk00000.dat.backup').rename(self.nodes[0].blocks_path / 'blk00000.dat')
+
+
 if __name__ == '__main__':
     GetblockstatsTest(__file__).main()