diff --git a/port_prediction.nim b/port_prediction.nim
index c291ca9..6b63659 100644
--- a/port_prediction.nim
+++ b/port_prediction.nim
@@ -1,10 +1,9 @@
 import algorithm
 import net
-import random
 import sequtils
 import unittest
 
-const RandomPortCount = 10000
+const RandomPortCount = 10000'u16
 
 proc min(a, b: uint16): uint16 =
   min(a.int32, b.int32).uint16
@@ -81,11 +80,13 @@ proc predictPortRange*(localPort: uint16, probedPorts: seq[uint16]): seq[uint16]
           result.add(maxPort.subtractOffset(i))
         return
   # assume symmetric NAT with random port mapping
-  randomize()
-  let first = if maxPort <= uint16.high - RandomPortCount - 1000'u16:
-    maxPort + 1000'u16
+  assert(RandomPortCount mod 2 == 0)
+  let center = minPort + (maxPort - minPort) div 2
+  let half = RandomPortCount div 2
+  let first = if (1024'u16 + half) < center:
+    min(center - half, uint16.high - RandomPortCount + 1)
   else:
-    uint16.high - RandomPortCount
+    1024'u16
   result = newSeq[uint16](RandomPortCount)
   for i in 0'u16 .. RandomPortCount - 1'u16:
     result[i] = first + i
@@ -155,5 +156,16 @@ suite "port prediction tests":
     check(predicted == @[Port(65533)])
 
   test "random mapping":
-    let predicted = predictPortRange(Port(1234), @[Port(3546), Port(7624)])
-    check(predicted.len == RandomPortCount)
+    let predicted = predictPortRange(Port(1234), @[Port(20000), Port(24000)])
+    let half = RandomPortCount div 2'u16
+    check(predicted == toSeq(countup(22000'u16 - half, 22000'u16 + half - 1)).map(toPort))
+
+  test "random mapping, low":
+    let predicted = predictPortRange(Port(1234), @[Port(1200), Port(1600)])
+    check(predicted.len == RandomPortCount.int)
+    check(predicted == toSeq(countup(1024'u16, 1024'u16 + RandomPortCount - 1)).map(toPort))
+
+  test "random mapping, high":
+    let predicted = predictPortRange(Port(1234), @[Port(65000), Port(65400)])
+    check(predicted.len == RandomPortCount.int)
+    check(predicted == toSeq(countup(uint16.high - RandomPortCount + 1, uint16.high)).map(toPort))