diff --git a/lib/src/main/java/com/ledmington/gal/Utils.java b/lib/src/main/java/com/ledmington/gal/Utils.java
index ed42745..8945d5a 100644
--- a/lib/src/main/java/com/ledmington/gal/Utils.java
+++ b/lib/src/main/java/com/ledmington/gal/Utils.java
@@ -36,25 +36,32 @@ public static <X> Supplier<X> weightedChoose(
             throw new IllegalArgumentException("The list of values cannot be empty");
         }
 
-        final Function<X, Double> safeWeight = x -> {
-            final double result = weight.apply(x);
-            if (result < 0.0) {
-                throw new IllegalArgumentException(String.format(
-                        "Negative weights are not allowed: the object '%s' produced the weight %f",
-                        x.toString(), result));
-            }
-            return result;
-        };
-        final double totalWeight =
-                values.stream().mapToDouble(safeWeight::apply).sum();
+        double minWeight = Double.POSITIVE_INFINITY;
+        double maxWeight = Double.NEGATIVE_INFINITY;
+        double totalWeight = 0.0;
+        for (final X x : values) {
+            final double w = weight.apply(x);
+            minWeight = Math.min(minWeight, w);
+            maxWeight = Math.max(maxWeight, w);
+            totalWeight += w;
+        }
+
+        if (minWeight == maxWeight) {
+            // if they all have the same weight, return a special function which treats all
+            // values equally
+            return () -> values.get(rng.nextInt(0, values.size()));
+        }
+
+        final double finalMinWeight = minWeight;
+        final double finalTotalWeight = totalWeight - finalMinWeight * values.size();
 
         return () -> {
-            final double chosenWeight = rng.nextDouble(0.0, totalWeight);
+            final double chosenWeight = rng.nextDouble(0.0, finalTotalWeight);
 
             double sum = 0.0;
             for (int i = 0; i < values.size() - 1; i++) {
                 final X ith_element = values.get(i);
-                sum += safeWeight.apply(ith_element);
+                sum += (weight.apply(ith_element) - finalMinWeight);
                 if (sum >= chosenWeight) {
                     return ith_element;
                 }
diff --git a/lib/src/test/java/com/ledmington/gal/TestUtils.java b/lib/src/test/java/com/ledmington/gal/TestUtils.java
index 27880c7..38f2157 100644
--- a/lib/src/test/java/com/ledmington/gal/TestUtils.java
+++ b/lib/src/test/java/com/ledmington/gal/TestUtils.java
@@ -25,6 +25,7 @@
 import java.util.List;
 import java.util.Map;
 import java.util.function.Function;
+import java.util.function.Supplier;
 import java.util.random.RandomGenerator;
 import java.util.random.RandomGeneratorFactory;
 import java.util.stream.IntStream;
@@ -86,8 +87,9 @@ public void weightsWork() {
             count.put(x, 0);
         }
 
+        final Supplier<Integer> weightedChoose = Utils.weightedChoose(values, w, rng);
         for (int i = 0; i < 10_000; i++) {
-            final Integer chosen = Utils.weightedChoose(values, w, rng).get();
+            final Integer chosen = weightedChoose.get();
             count.put(chosen, count.get(chosen) + 1);
         }
 
@@ -106,11 +108,33 @@ public void weightsWork() {
     }
 
     @Test
-    public void negativeWeightsDoNotWork() {
+    public void negativeWeightsWorkAsWell() {
         final List<Integer> values = List.of(1, 2, 3, 4, 5, 6, 7, 8, 9);
         final Function<Integer, Double> w = x -> -(double) x;
 
-        assertThrows(IllegalArgumentException.class, () -> Utils.weightedChoose(values, w, rng));
+        final Map<Integer, Integer> count = new HashMap<>();
+        for (final Integer x : values) {
+            count.put(x, 0);
+        }
+
+        final Supplier<Integer> weightedChoose = Utils.weightedChoose(values, w, rng);
+        for (int i = 0; i < 10_000; i++) {
+            final Integer chosen = weightedChoose.get();
+            count.put(chosen, count.get(chosen) + 1);
+        }
+
+        for (int i = 0; i < values.size() - 1; i++) {
+            final Integer first = values.get(i);
+            final Integer second = values.get(i + 1);
+            assertTrue(
+                    count.get(first) > 0,
+                    String.format("Value %d (with weight %f) did not appear once", first, w.apply(first)));
+            assertTrue(
+                    count.get(first) < count.get(second),
+                    String.format(
+                            "Value %d (with weight %f) appeared more often than value %d (with weight %f): %,d > %,d",
+                            first, w.apply(first), second, w.apply(second), count.get(first), count.get(second)));
+        }
     }
 
     @Test