diff --git a/src/reduction/bit_depth.rs b/src/reduction/bit_depth.rs
index df99973c..ee3f0665 100644
--- a/src/reduction/bit_depth.rs
+++ b/src/reduction/bit_depth.rs
@@ -2,23 +2,62 @@ use bit_vec::BitVec;
 use colors::{BitDepth, ColorType};
 use png::PngData;
 
+const ONE_BIT_PERMUTATIONS: [u8; 2] = [0b0000_0000, 0b1111_1111];
+const TWO_BIT_PERMUTATIONS: [u8; 5] = [
+    0b0000_0000,
+    0b0000_1111,
+    0b0011_1100,
+    0b1111_0000,
+    0b1111_1111,
+];
+const FOUR_BIT_PERMUTATIONS: [u8; 11] = [
+    0b0000_0000,
+    0b0000_0011,
+    0b0000_1100,
+    0b0011_0000,
+    0b1100_0000,
+    0b0000_1111,
+    0b0011_1100,
+    0b1111_0000,
+    0b0011_1111,
+    0b1111_1100,
+    0b1111_1111,
+];
+
 pub fn reduce_bit_depth_8_or_less(png: &mut PngData) -> bool {
     let mut reduced = BitVec::with_capacity(png.raw_data.len() * 8);
     let bit_depth: usize = png.ihdr_data.bit_depth.as_u8() as usize;
     let mut allowed_bits = 1;
     for line in png.scan_lines() {
         let bit_vec = BitVec::from_bytes(&line.data);
-        for (i, bit) in bit_vec.iter().enumerate() {
-            let bit_index = if png.ihdr_data.color_type == ColorType::Indexed {
-                bit_depth - (i % bit_depth)
-            } else {
-                i % bit_depth
-            };
-            if bit && bit_index > allowed_bits {
-                allowed_bits = bit_index.next_power_of_two();
-                if allowed_bits == bit_depth {
-                    // Not reducable
-                    return false;
+        if png.ihdr_data.color_type == ColorType::Indexed {
+            for (i, bit) in bit_vec.iter().enumerate() {
+                let bit_index = bit_depth - (i % bit_depth);
+                if bit && bit_index > allowed_bits {
+                    allowed_bits = bit_index.next_power_of_two();
+                    if allowed_bits == bit_depth {
+                        // Not reducable
+                        return false;
+                    }
+                }
+            }
+        } else {
+            for byte in bit_vec.to_bytes() {
+                while allowed_bits < bit_depth {
+                    let permutations: &[u8] = if allowed_bits == 1 {
+                        &ONE_BIT_PERMUTATIONS
+                    } else if allowed_bits == 2 {
+                        &TWO_BIT_PERMUTATIONS
+                    } else if allowed_bits == 4 {
+                        &FOUR_BIT_PERMUTATIONS
+                    } else {
+                        return false;
+                    };
+                    if permutations.iter().any(|perm| *perm == byte) {
+                        break;
+                    } else {
+                        allowed_bits <<= 1;
+                    }
                 }
             }
         }
diff --git a/tests/files/issue-140.png b/tests/files/issue-140.png
new file mode 100644
index 00000000..12e9d2a4
Binary files /dev/null and b/tests/files/issue-140.png differ
diff --git a/tests/regression.rs b/tests/regression.rs
index 5a1855a8..ea3ecf24 100644
--- a/tests/regression.rs
+++ b/tests/regression.rs
@@ -536,3 +536,15 @@ fn issue_133_left() {
         BitDepth::Eight,
     );
 }
+
+#[test]
+fn issue_140() {
+    test_it_converts(
+        "tests/files/issue-140.png",
+        None,
+        ColorType::Grayscale,
+        BitDepth::Two,
+        ColorType::Grayscale,
+        BitDepth::Two,
+    );
+}