diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0aac5423..ee3258c8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,7 @@
     trials for optimizing the alpha channel, using the previously mentioned fast heuristic.
     This option will make optimization of images with transparency somewhat slower,
     but may improve compression.
+ - Fixed a bug in reducing palettes for images with bit depth of two([#80](https://github.com/shssoichiro/oxipng/issues/80))
  - Code cleanup
 
 ### Version 0.16.3
diff --git a/src/png.rs b/src/png.rs
index 0c0f19c4..5449d8a3 100644
--- a/src/png.rs
+++ b/src/png.rs
@@ -543,7 +543,7 @@ impl PngData {
                     for (i, bit) in bitvec.iter().enumerate() {
                         let mod_i = i % 4;
                         if bit {
-                            current += 2u8.pow(3u32 - mod_i as u32);
+                            current += 1u8 << (3 - mod_i);
                         }
                         if mod_i == 3 {
                             seen.insert(current);
@@ -557,7 +557,7 @@ impl PngData {
                     for (i, bit) in bitvec.iter().enumerate() {
                         let mod_i = i % 2;
                         if bit {
-                            current += 2u8.pow(1u32 - mod_i as u32);
+                            current += 1u8 << (1 - mod_i);
                         }
                         if mod_i == 1 {
                             seen.insert(current);
@@ -649,17 +649,17 @@ impl PngData {
                     new_byte |= if let Some(new_idx) = index_map.get(&one) {
                         *new_idx << 6
                     } else {
-                        one << 6
+                        one
                     };
                     new_byte |= if let Some(new_idx) = index_map.get(&two) {
                         *new_idx << 4
                     } else {
-                        two << 4
+                        two
                     };
                     new_byte |= if let Some(new_idx) = index_map.get(&three) {
                         *new_idx << 2
                     } else {
-                        three << 2
+                        three
                     };
                     new_byte |= if let Some(new_idx) = index_map.get(&four) {
                         *new_idx
diff --git a/tests/files/issue-80.png b/tests/files/issue-80.png
new file mode 100644
index 00000000..15c81914
Binary files /dev/null and b/tests/files/issue-80.png differ
diff --git a/tests/regression.rs b/tests/regression.rs
index d8cf6d65..aaa63820 100644
--- a/tests/regression.rs
+++ b/tests/regression.rs
@@ -274,3 +274,20 @@ fn issue_60() {
         BitDepth::Eight,
     );
 }
+
+#[test]
+fn issue_80() {
+    let input = PathBuf::from("tests/files/issue-80.png");
+    let opts = get_opts(&input);
+    let output = opts.out_file.clone();
+
+    test_it_converts(
+        &input,
+        &output,
+        &opts,
+        ColorType::Indexed,
+        BitDepth::Two,
+        ColorType::Indexed,
+        BitDepth::One,
+    );
+}