diff --git a/test/functional/test_framework/messages.py b/test/functional/test_framework/messages.py
index b4a5d9d5efa69..eb8d0df5a7002 100755
--- a/test/functional/test_framework/messages.py
+++ b/test/functional/test_framework/messages.py
@@ -815,10 +815,12 @@ def is_valid(self):
             return False
         return True
 
-    def solve(self):
+    def solve(self, multiplier = 1):
+        # If a multiplier is provided, ensure work is between
+        # multiplier * target and multiplier / 2 * target
         self.rehash()
         target = uint256_from_compact(self.nBits)
-        while self.sha256 > target:
+        while self.sha256 > target * multiplier or (multiplier != 1 and self.sha256 <= target * multiplier / 4):
             self.nNonce += 1
             self.rehash()