diff --git a/src/Qir/Tests/QIR-static/qir-test-math.cpp b/src/Qir/Tests/QIR-static/qir-test-math.cpp
index b544ce5c6a1..545d869c436 100644
--- a/src/Qir/Tests/QIR-static/qir-test-math.cpp
+++ b/src/Qir/Tests/QIR-static/qir-test-math.cpp
@@ -116,6 +116,12 @@ TEST_CASE("QIR: Math.DrawRandomInt", "[qir.math][qir.Math.DrawRandomInt]")
         REQUIRE(0 == strcmp(exc.what(), Quantum::Qis::Internal::excStrDrawRandomVal));
     }
 
+    // Test equal minimum and maximum:
+    for(uint64_t num: { -5, 0, 3 } )
+    {
+        REQUIRE(Microsoft__Quantum__Testing__QIR__Math__TestDrawRandomInt__body(num, num) == num);
+    }
+
     // There is a strong difference in the opinions about how the random number generator must be tested.
     // More or less agreed-upon items are:
     //  * The test must be 100% deterministic, i.e. must not fail, even with a very low probability. 
diff --git a/src/Simulation/QSharpFoundation/Random/Intrinsic.qs b/src/Simulation/QSharpFoundation/Random/Intrinsic.qs
index df6dc83534e..2232e824088 100644
--- a/src/Simulation/QSharpFoundation/Random/Intrinsic.qs
+++ b/src/Simulation/QSharpFoundation/Random/Intrinsic.qs
@@ -17,7 +17,7 @@ namespace Microsoft.Quantum.Random {
     /// probability.
     ///
     /// # Remarks
-    /// Fails if `max <= min`.
+    /// Fails if `max < min`.
     ///
     /// # Example
     /// The following Q# snippet randomly rolls a six-sided die:
@@ -45,7 +45,7 @@ namespace Microsoft.Quantum.Random {
     /// uniform probability.
     ///
     /// # Remarks
-    /// Fails if `max <= min`.
+    /// Fails if `max < min`.
     ///
     /// # Example
     /// The following Q# snippet randomly draws an angle between $0$ and $2 \pi$:
diff --git a/src/Simulation/QSharpFoundation/Random/Uniform.qs b/src/Simulation/QSharpFoundation/Random/Uniform.qs
index 34c65b39e5e..4e818c4a91f 100644
--- a/src/Simulation/QSharpFoundation/Random/Uniform.qs
+++ b/src/Simulation/QSharpFoundation/Random/Uniform.qs
@@ -20,7 +20,7 @@ namespace Microsoft.Quantum.Random {
     /// interval from `min` to `max` with uniform probability.
     ///
     /// # Remarks
-    /// Fails if `max <= min`.
+    /// Fails if `max < min`.
     ///
     /// # Example
     /// The following Q# snippet randomly draws an angle between $0$ and $2 \pi$:
@@ -34,7 +34,7 @@ namespace Microsoft.Quantum.Random {
     function ContinuousUniformDistribution(
         min : Double, max : Double
     ) : ContinuousDistribution {
-        Fact(max > min, $"Max must be larger than min, but {max} <= {min}.");
+        Fact(max >= min, $"Max must be greater than or equal to min, but {max} < {min}.");
         return ContinuousDistribution(Delay(DrawRandomDouble, (min, max), _));
     }
 
@@ -52,7 +52,7 @@ namespace Microsoft.Quantum.Random {
     /// range from `min` to `max` with uniform probability.
     ///
     /// # Remarks
-    /// Fails if `max <= min`.
+    /// Fails if `max < min`.
     ///
     /// # Example
     /// The following Q# snippet randomly rolls a six-sided die:
@@ -64,7 +64,7 @@ namespace Microsoft.Quantum.Random {
     /// # See Also
     /// - Microsoft.Quantum.DrawRandomDouble
     function DiscreteUniformDistribution(min : Int, max : Int) : DiscreteDistribution {
-        Fact(max > min, $"Max must be larger than min, but {max} <= {min}.");
+        Fact(max >= min, $"Max must be greater than or equal to min, but {max} < {min}.");
         return DiscreteDistribution(Delay(DrawRandomInt, (min, max), _));
     }
 
diff --git a/src/Simulation/Simulators.Tests/TestProjects/IntrinsicTests/Random/Tests.qs b/src/Simulation/Simulators.Tests/TestProjects/IntrinsicTests/Random/Tests.qs
index aff82adbc8a..c646960b606 100644
--- a/src/Simulation/Simulators.Tests/TestProjects/IntrinsicTests/Random/Tests.qs
+++ b/src/Simulation/Simulators.Tests/TestProjects/IntrinsicTests/Random/Tests.qs
@@ -74,10 +74,25 @@ namespace Microsoft.Quantum.Tests {
     @Test("QuantumSimulator")
     @Test("ToffoliSimulator")
     operation CheckDrawRandomIntObeysRanges() : Unit {
-        let randomInt = DrawRandomInt(0, 45);
+        mutable randomInt = DrawRandomInt(0, 45);
         if (randomInt > 45 or randomInt < 0) {
             fail $"DrawRandomInt(0, 45) returned {randomInt}, outside the allowed range.";
         }
+
+        set randomInt = DrawRandomInt(0, 0);
+        if (randomInt > 0 or randomInt < 0) {
+            fail $"DrawRandomInt(0, 0) returned {randomInt}, outside the allowed range.";
+        }
+
+        set randomInt = DrawRandomInt(-3, -3);
+        if (randomInt > -3 or randomInt < -3) {
+            fail $"DrawRandomInt(-3, -3) returned {randomInt}, outside the allowed range.";
+        }
+
+        set randomInt = DrawRandomInt(3, 3);
+        if (randomInt > 3 or randomInt < 3) {
+            fail $"DrawRandomInt(3, 3) returned {randomInt}, outside the allowed range.";
+        }
     }
     
     /// # Summary
diff --git a/src/Simulation/Simulators/QuantumSimulator/SimulatorBase.cs b/src/Simulation/Simulators/QuantumSimulator/SimulatorBase.cs
index c84cb17936f..8ef72b66aa0 100644
--- a/src/Simulation/Simulators/QuantumSimulator/SimulatorBase.cs
+++ b/src/Simulation/Simulators/QuantumSimulator/SimulatorBase.cs
@@ -469,16 +469,16 @@ public DrawRandomInt(SimulatorBase m) : base(m) =>
             public override Func<(long, long), long> __Body__ => arg =>
             {
                 var (min, max) = arg;
-                if (max <= min)
+                if (max < min)
                 {
-                    throw new ExecutionFailException($"Max must be greater than min, but {max} <= {min}.");
+                    throw new ExecutionFailException($"Max must be greater than or equal to min, but {max} < {min}.");
                 }
                 return sim.RandomGenerator.NextLong(min, max);
             };
         }
 
         /// <summary>
-        ///     Implements the DrawRandomInt operation from the
+        ///     Implements the DrawRandomDouble operation from the
         ///     Microsoft.Quantum.Random namespace.
         /// </summary>
         public class DrawRandomDouble : Random.DrawRandomDouble
@@ -490,9 +490,9 @@ public DrawRandomDouble(SimulatorBase m) : base(m) =>
             public override Func<(double, double), double> __Body__ => arg =>
             {
                 var (min, max) = arg;
-                if (max <= min)
+                if (max < min)
                 {
-                    throw new ExecutionFailException($"Max must be greater than min, but {max} <= {min}.");
+                    throw new ExecutionFailException($"Max must be greater than or equal to min, but {max} < {min}.");
                 }
                 var delta = max - min;
                 return min + delta * sim.RandomGenerator.NextDouble();