diff --git a/lslopt/lslfuncopt.py b/lslopt/lslfuncopt.py
index e7bc4c2..4c71c53 100644
--- a/lslopt/lslfuncopt.py
+++ b/lslopt/lslfuncopt.py
@@ -528,6 +528,12 @@ def OptimizeFunc(self, parent, index):
             parent[index] = nr(nt='CONST', t='list', value=[], SEF=True)
             return
 
+    if name == 'llFrand' and child[0].nt == 'CONST':
+        # We can set a range when the input is a constant
+        value = child[0].value
+        node.min = lslfuncs.F32(min(value, 0) * 0.9999999403953552)
+        node.max = lslfuncs.F32(max(value, 0) * 0.9999999403953552)
+
 def FuncOptSetup():
     # Patch the default values list for LSO
     if lslcommon.LSO:
diff --git a/unit_tests/expr.suite/llfrand-1.lsl b/unit_tests/expr.suite/llfrand-1.lsl
index 6b00c35..9cad062 100644
--- a/unit_tests/expr.suite/llfrand-1.lsl
+++ b/unit_tests/expr.suite/llfrand-1.lsl
@@ -1,3 +1,4 @@
+// Test that there's at least one 7-digit number
 [ llFrand(16777216)
 , llFrand(16777216)
 , llFrand(16777216)
diff --git a/unit_tests/expr.suite/llfrand-2.lsl b/unit_tests/expr.suite/llfrand-2.lsl
index 6b00c35..b1873ba 100644
--- a/unit_tests/expr.suite/llfrand-2.lsl
+++ b/unit_tests/expr.suite/llfrand-2.lsl
@@ -1,3 +1,4 @@
+// Test that there's at least one 8-digit number
 [ llFrand(16777216)
 , llFrand(16777216)
 , llFrand(16777216)
diff --git a/unit_tests/expr.suite/llfrand-3.lsl b/unit_tests/expr.suite/llfrand-3.lsl
new file mode 100644
index 0000000..7b36c3f
--- /dev/null
+++ b/unit_tests/expr.suite/llfrand-3.lsl
@@ -0,0 +1,23 @@
+[ llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+, llFrand(-5)
+, llFrand(-5.0)
+]
diff --git a/unit_tests/expr.suite/llfrand-3.out b/unit_tests/expr.suite/llfrand-3.out
new file mode 100644
index 0000000..ece9add
--- /dev/null
+++ b/unit_tests/expr.suite/llfrand-3.out
@@ -0,0 +1,3 @@
+REGEX
+(?:[\[,] -[0-4]\.[0-9]*
+){22}\]
\ No newline at end of file
diff --git a/unit_tests/regression.suite/llfrand.lsl b/unit_tests/regression.suite/llfrand.lsl
new file mode 100644
index 0000000..4f577a6
--- /dev/null
+++ b/unit_tests/regression.suite/llfrand.lsl
@@ -0,0 +1,20 @@
+default { timer() {
+    llParticleSystem(
+         [ llFrand(-5)
+         , llFrand(-5) > -5
+         , llFrand(-5) <= 0
+         , llFrand(-5) > 0
+         , llFrand(-5.)
+         , llFrand(-16777216)
+         , llFrand(-16777216.)
+         , llFrand(5)
+         , llFrand(5) < 5
+         , llFrand(5) >= 0
+         , llFrand(5) < 0
+         , llFrand(5.)
+         , llFrand(16777216)
+         , llFrand(16777216.)
+         , llFrand(33554433)
+         , llFrand(33554433.)
+     ]);
+}}
diff --git a/unit_tests/regression.suite/llfrand.out b/unit_tests/regression.suite/llfrand.out
new file mode 100644
index 0000000..19ae702
--- /dev/null
+++ b/unit_tests/regression.suite/llfrand.out
@@ -0,0 +1,24 @@
+default
+{
+    timer()
+    {
+        llParticleSystem(
+            [ llFrand(((integer)-5))
+            , 1
+            , 1
+            , 0
+            , llFrand(((float)-5))
+            , llFrand(((integer)-16777216))
+            , llFrand(((float)-16777216))
+            , llFrand(5)
+            , 1
+            , 1
+            , 0
+            , llFrand(((float)5))
+            , llFrand(16777216)
+            , llFrand(((float)16777216))
+            , llFrand(33554433)
+            , llFrand(((float)33554432))
+            ]);
+    }
+}
diff --git a/unit_tests/regression.suite/llfrand.run b/unit_tests/regression.suite/llfrand.run
new file mode 100644
index 0000000..6e609ff
--- /dev/null
+++ b/unit_tests/regression.suite/llfrand.run
@@ -0,0 +1 @@
+main.py -O -listadd -
\ No newline at end of file