diff --git a/lib/pure/bitops.nim b/lib/pure/bitops.nim
index 9ebdabb7b..e00ea3109 100644
--- a/lib/pure/bitops.nim
+++ b/lib/pure/bitops.nim
@@ -355,6 +355,15 @@ proc firstSetBit*(x: SomeInteger): int {.inline, noSideEffect.} =
       when sizeof(x) <= 4: result = firstSetBitNim(x.uint32)
       else: result = firstSetBitNim(x.uint64)
 
+proc lastSetBit*(x: SomeUnsignedInt): uint {.inline, noSideEffect.} =
+  ## Returns the 1-based index of the most significant set bit of x.
+  ## If x == 0, the result will also be 0
+  var temp = x
+  result = 0
+  while temp != 0:
+    temp = temp shr 1
+    result += 1
+
 proc fastLog2*(x: SomeInteger): int {.inline, noSideEffect.} =
   ## Quickly find the log base 2 of an integer.
   ## If `x` is zero, when ``noUndefinedBitOpts`` is set, result is -1,
diff --git a/lib/pure/collections/hashcommon.nim b/lib/pure/collections/hashcommon.nim
index d9a914afc..6281074af 100644
--- a/lib/pure/collections/hashcommon.nim
+++ b/lib/pure/collections/hashcommon.nim
@@ -9,6 +9,7 @@
 
 # An ``include`` file which contains common code for
 # hash sets and tables.
+from bitops import lastSetBit
 
 const
   growthFactor = 2
@@ -51,7 +52,7 @@ proc rawGetKnownHC[X, A](t: X, key: A, hc: Hash): int {.inline.} =
   rawGetKnownHCImpl()
 
 template genHashImpl(key, hc: typed) =
-  hc = hash(key)
+  hc = hash(key, targetBits=lastSetBit(maxHash(t).uint))
   if hc == 0: # This almost never taken branch should be very predictable.
     hc = 314159265 # Value doesn't matter; Any non-zero favorite is fine.
 
diff --git a/lib/pure/hashes.nim b/lib/pure/hashes.nim
index ac8498517..9a511ce9d 100644
--- a/lib/pure/hashes.nim
+++ b/lib/pure/hashes.nim
@@ -113,31 +113,65 @@ proc hash*[T: proc](x: T): Hash {.inline.} =
     result = hash(pointer(x))
 
 const
-  prime = uint(11)
+  defaultSeedA = (17316035218449499591'u64).uint
+  defaultSeedB = (1734880652122947187'u64).uint
 
-proc hash*(x: int): Hash {.inline.} =
+template computeIntegerHash(x, numBits, seedA, seedB): Hash =
+  cast[Hash]((seedA*cast[uint](x) + seedB) shr (sizeof(x)*8 - numBits*8))
+
+proc hash*(
+  x: int,
+  targetBits: SomeUnsignedInt = sizeof(uint),
+  seedA = defaultSeedA,
+  seedB = defaultSeedB
+): Hash {.inline.} =
   ## Efficient hashing of integers.
-  result = cast[Hash](cast[uint](x) * prime)
+  result = computeIntegerHash(x, targetBits, seedA, seedB)
 
-proc hash*(x: int64): Hash {.inline.} =
+proc hash*(
+  x: int64,
+  targetBits: SomeUnsignedInt = sizeof(uint),
+  seedA = defaultSeedA,
+  seedB = defaultSeedB
+): Hash {.inline.} =
   ## Efficient hashing of `int64` integers.
-  result = cast[Hash](cast[uint](x) * prime)
+  result = computeIntegerHash(x, targetBits, seedA, seedB)
 
-proc hash*(x: uint): Hash {.inline.} =
+proc hash*(
+  x: uint,
+  targetBits: SomeUnsignedInt = sizeof(uint),
+  seedA = defaultSeedA,
+  seedB = defaultSeedB
+): Hash {.inline.} =
   ## Efficient hashing of unsigned integers.
-  result = cast[Hash](x * prime)
+  result = computeIntegerHash(x, targetBits, seedA, seedB)
 
-proc hash*(x: uint64): Hash {.inline.} =
+proc hash*(
+  x: uint64,
+  targetBits: SomeUnsignedInt = sizeof(uint),
+  seedA = defaultSeedA,
+  seedB = defaultSeedB
+): Hash {.inline.} =
   ## Efficient hashing of `uint64` integers.
-  result = cast[Hash](cast[uint](x) * prime)
+  result = computeIntegerHash(x, targetBits, seedA, seedB)
 
-proc hash*(x: char): Hash {.inline.} =
+proc hash*(
+  x: char,
+  targetBits: SomeUnsignedInt = sizeof(uint),
+  seedA = defaultSeedA,
+  seedB = defaultSeedB
+): Hash {.inline.} =
   ## Efficient hashing of characters.
-  result = cast[Hash](cast[uint](ord(x)) * prime)
+  result = computeIntegerHash(ord(x), targetBits, seedA, seedB)
 
-proc hash*[T: Ordinal](x: T): Hash {.inline.} =
+proc hash*[T: Ordinal](
+  x: T,
+  targetBits: SomeUnsignedInt = sizeof(uint),
+  seedA = defaultSeedA,
+  seedB = defaultSeedB
+): Hash {.inline.} =
   ## Efficient hashing of other ordinal types (e.g. enums).
-  result = cast[Hash](cast[uint](ord(x)) * prime)
+  result = computeIntegerHash(x, targetBits, seedA, seedB)
 
 proc hash*(x: float): Hash {.inline.} =
   ## Efficient hashing of floats.
diff --git a/tests/collections/thashsets.nim b/tests/collections/thashsets.nim
index cd4401511..bccf4654f 100644
--- a/tests/collections/thashsets.nim
+++ b/tests/collections/thashsets.nim
@@ -1,4 +1,4 @@
-import sets, hashes, algorithm
+import sets, hashes, algorithm, bitops
 
 
 block setEquality:
@@ -120,3 +120,13 @@ block hashForOrderdSet:
   reversed = !$reversed
   doAssert hash(r) == reversed
   doAssert hash(s1) != reversed
+
+block hashDoesntHaveLowerBitsCleared:
+  let num32 = 0xFFFF.uint32
+  let bits = num32.lastBitSet
+
+  let h1 = hash(0xFFFFFFFF00000000'u64, targetBits=bits)
+  let h2 = hash(0x2345123400000000'u64, targetBits=bits)
+
+
+  doAssert (h1 and num32) != (h2 and num32)