diff --git a/.travis.yml b/.travis.yml
index f3548d3c..626b2b9d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,7 +11,7 @@ matrix:
       env: TARGET=x86_64-apple-darwin
       cache: cargo
     - os: linux
-      rust: 1.34.0
+      rust: 1.36.0
       env: TARGET=x86_64-unknown-linux-gnu
       cache: cargo
     - os: linux
diff --git a/README.md b/README.md
index dbb9ebfd..b3d252c7 100644
--- a/README.md
+++ b/README.md
@@ -26,7 +26,7 @@ cargo build --release
 cp target/release/oxipng /usr/local/bin
 ```
 
-The current minimum supported Rust version is **1.34.0**. Oxipng may compile on earlier versions of Rust,
+The current minimum supported Rust version is **1.36.0**. Oxipng may compile on earlier versions of Rust,
 but there is no guarantee.
 
 Oxipng follows Semantic Versioning.
diff --git a/src/reduction/mod.rs b/src/reduction/mod.rs
index 8401b539..88ff72c4 100644
--- a/src/reduction/mod.rs
+++ b/src/reduction/mod.rs
@@ -61,9 +61,24 @@ pub fn reduced_palette(png: &PngImage) -> Option<PngImage> {
             }
         }
 
+        let mut used_enumerated : Vec<(usize, &bool)>= used.iter().enumerate().collect();
+        used_enumerated.sort_by(|a, b| {
+            //Sort by ascending alpha and descending luma.
+            let color_val = |i| {
+                let color = palette.get(i).copied()
+                    .unwrap_or_else(|| RGBA8::new(0, 0, 0, 255));
+                ((color.a as i32) << 18)
+                // These are coefficients for standard sRGB to luma conversion
+                - (color.r as i32) * 299
+                - (color.g as i32) * 587
+                - (color.b as i32) * 114
+            };
+            color_val(a.0).cmp(&color_val(b.0))
+        });
+
         let mut next_index = 0u16;
         let mut seen = HashMap::with_capacity(palette.len());
-        for (i, (used, palette_map)) in used.iter().cloned().zip(palette_map.iter_mut()).enumerate()
+        for (i, used) in used_enumerated.iter().cloned()
         {
             if !used {
                 continue;
@@ -75,12 +90,12 @@ pub fn reduced_palette(png: &PngImage) -> Option<PngImage> {
                 .unwrap_or_else(|| RGBA8::new(0, 0, 0, 255));
             match seen.entry(color) {
                 Vacant(new) => {
-                    *palette_map = Some(next_index as u8);
+                    palette_map[i] = Some(next_index as u8);
                     new.insert(next_index as u8);
                     next_index += 1;
                 }
                 Occupied(remap_to) => {
-                    *palette_map = Some(*remap_to.get());
+                    palette_map[i] = Some(*remap_to.get())
                 }
             }
         }
@@ -211,6 +226,14 @@ pub fn reduce_color_type(png: &PngImage) -> Option<PngImage> {
         }
     }
 
+    //Make sure that palette gets sorted. Ideally, this should be done within reduced_color_to_palette.
+    if should_reduce_bit_depth && reduced.ihdr.color_type == ColorType::Indexed {
+        if let Some(r) = reduced_palette(&reduced) {
+            reduced = Cow::Owned(r);
+            should_reduce_bit_depth = true;
+        }
+    }
+
     if should_reduce_bit_depth {
         // Some conversions will allow us to perform bit depth reduction that
         // wasn't possible before