diff --git a/ulid.go b/ulid.go
index e07e1a6..8bbda1b 100644
--- a/ulid.go
+++ b/ulid.go
@@ -641,7 +641,7 @@ func (m *MonotonicEntropy) increment() error {
 	return nil
 }
 
-// random returns a uniform random value in [1, m.inc), reading entropy
+// random returns a uniform random value in [1, m.inc], reading entropy
 // from m.Reader. When m.inc == 0 || m.inc == 1, it returns 1.
 // Adapted from: https://golang.org/pkg/crypto/rand/#Int
 func (m *MonotonicEntropy) random() (inc uint64, err error) {
@@ -651,7 +651,7 @@ func (m *MonotonicEntropy) random() (inc uint64, err error) {
 
 	// Fast path for using a underlying rand.Rand directly.
 	if m.rng != nil {
-		// Range: [1, m.inc)
+		// Range: [1, m.inc]
 		return 1 + uint64(m.rng.Int63n(int64(m.inc))), nil
 	}
 
@@ -667,7 +667,7 @@ func (m *MonotonicEntropy) random() (inc uint64, err error) {
 		msbitLen = 8
 	}
 
-	for inc == 0 || inc >= m.inc {
+	for {
 		if _, err = io.ReadFull(m.Reader, m.rand[:byteLen]); err != nil {
 			return 0, err
 		}
@@ -688,9 +688,14 @@ func (m *MonotonicEntropy) random() (inc uint64, err error) {
 		case 5, 6, 7, 8:
 			inc = uint64(binary.LittleEndian.Uint64(m.rand[:8]))
 		}
+
+		// inc may exceed m.inc; redraw rather than bias the low end of the range.
+		if inc < m.inc {
+			break
+		}
 	}
 
-	// Range: [1, m.inc)
+	// Range: [1, m.inc]
 	return 1 + inc, nil
 }
 
diff --git a/ulid_test.go b/ulid_test.go
index afa194b..7c4bf90 100644
--- a/ulid_test.go
+++ b/ulid_test.go
@@ -19,6 +19,7 @@ import (
 	"fmt"
 	"io"
 	"math"
+	"math/big"
 	"math/rand"
 	"strings"
 	"testing"
@@ -629,6 +630,49 @@ func TestMonotonic(t *testing.T) {
 	}
 }
 
+// Regression test: random() rejected a masked draw of 0, making an
+// increment of 1 unreachable and inc == 2 fully deterministic. The reader
+// yields an exact byte sequence so the result does not depend on chance.
+func TestMonotonicIncrementRange(t *testing.T) {
+	t.Parallel()
+
+	// The first 10 bytes seed the first ULID; the rest are consumed by random().
+	seed := append([]byte{0x01}, bytes.Repeat([]byte{0x00}, 9)...)
+	draws := []byte{0x00, 0x01, 0x02, 0x03, 0x00}
+	reader := bytes.NewReader(append(seed, draws...))
+
+	entropy := ulid.Monotonic(reader, 2)
+
+	prev, err := ulid.New(123, entropy)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	// masked 0 and 1 are accepted as increments 1 and 2; 2 and 3 are redrawn
+	wantDeltas := []uint64{1, 2, 1}
+
+	for i, want := range wantDeltas {
+		next, err := ulid.New(123, entropy)
+		if err != nil {
+			t.Fatalf("draw %d: %v", i, err)
+		}
+
+		if prev.Compare(next) >= 0 {
+			t.Fatalf("draw %d: monotonicity violated: prev=%v next=%v", i, prev, next)
+		}
+
+		delta := new(big.Int).Sub(
+			new(big.Int).SetBytes(next.Entropy()),
+			new(big.Int).SetBytes(prev.Entropy()),
+		).Uint64()
+		if delta != want {
+			t.Fatalf("draw %d: delta = %d, want %d", i, delta, want)
+		}
+
+		prev = next
+	}
+}
+
 func TestMonotonicOverflow(t *testing.T) {
 	t.Parallel()