diff --git a/src/lib.rs b/src/lib.rs
index a9d456ba..226bdf86 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -14,7 +14,7 @@ use crate::reduction::*;
 use crc::crc32;
 use image::{DynamicImage, GenericImageView, ImageFormat, Pixel};
 use rayon::prelude::*;
-use std::collections::{HashMap, HashSet};
+use std::collections::{BTreeMap, HashMap, HashSet};
 use std::fmt;
 use std::fs::{copy, File};
 use std::io::{stdin, stdout, BufWriter, Read, Write};
@@ -843,11 +843,15 @@ fn perform_strip(png: &mut PngData, opts: &Options) {
         // Strip headers
         Headers::None => (),
         Headers::Keep(ref hdrs) => {
-            raw.aux_headers.retain(|chunk, _| {
-                std::str::from_utf8(chunk)
+            let keys: Vec<[u8; 4]> = raw.aux_headers.keys().cloned().collect();
+            for hdr in &keys {
+                let preserve = std::str::from_utf8(hdr)
                     .ok()
-                    .map_or(false, |name| hdrs.contains(name))
-            });
+                    .map_or(false, |name| hdrs.contains(name));
+                if !preserve {
+                    raw.aux_headers.remove(hdr);
+                }
+            }
         }
         Headers::Strip(ref hdrs) => {
             for hdr in hdrs {
@@ -859,11 +863,14 @@ fn perform_strip(png: &mut PngData, opts: &Options) {
                 *b"cHRM", *b"gAMA", *b"iCCP", *b"sBIT", *b"sRGB", *b"bKGD", *b"hIST", *b"pHYs",
                 *b"sPLT",
             ];
-            raw.aux_headers
-                .retain(|hdr, _| PRESERVED_HEADERS.contains(hdr));
+            for hdr in &PRESERVED_HEADERS {
+                if !PRESERVED_HEADERS.contains(hdr) {
+                    raw.aux_headers.remove(hdr);
+                }
+            }
         }
         Headers::All => {
-            raw.aux_headers = HashMap::new();
+            raw.aux_headers = BTreeMap::new();
         }
     }
 
diff --git a/src/png/mod.rs b/src/png/mod.rs
index 6d46670e..2fd5184f 100644
--- a/src/png/mod.rs
+++ b/src/png/mod.rs
@@ -8,7 +8,7 @@ use byteorder::{BigEndian, WriteBytesExt};
 use crc::crc32;
 use rgb::ComponentSlice;
 use rgb::RGBA8;
-use std::collections::HashMap;
+use std::collections::BTreeMap;
 use std::fs::File;
 use std::io::{Read, Seek, SeekFrom};
 use std::iter::Iterator;
@@ -38,7 +38,7 @@ pub struct PngImage {
     /// The pixel value that should be rendered as transparent
     pub transparency_pixel: Option<Vec<u8>>,
     /// All non-critical headers from the PNG are stored here
-    pub aux_headers: HashMap<[u8; 4], Vec<u8>>,
+    pub aux_headers: BTreeMap<[u8; 4], Vec<u8>>,
 }
 
 /// Contains all data relevant to a PNG image
@@ -97,7 +97,7 @@ impl PngData {
         }
         byte_offset += 8;
         // Read the data headers
-        let mut aux_headers: HashMap<[u8; 4], Vec<u8>> = HashMap::new();
+        let mut aux_headers: BTreeMap<[u8; 4], Vec<u8>> = BTreeMap::new();
         let mut idat_headers: Vec<u8> = Vec::new();
         while let Some(header) = parse_next_header(byte_data, &mut byte_offset, fix_errors)? {
             match &header.name {