diff --git a/src/evaluate.rs b/src/evaluate.rs
index adeef359..5260bc2d 100644
--- a/src/evaluate.rs
+++ b/src/evaluate.rs
@@ -19,7 +19,7 @@ use std::thread;
 /// Collect image versions and pick one that compresses best
 pub struct Evaluator {
     /// images are sent to the thread for evaluation
-    eval_send: Option<SyncSender<(Arc<PngImage>, bool)>>,
+    eval_send: Option<SyncSender<(Arc<PngImage>, f32, bool)>>,
     // the thread helps evaluate images asynchronously
     eval_thread: thread::JoinHandle<Option<PngData>>,
 }
@@ -43,24 +43,26 @@ impl Evaluator {
 
     /// Set baseline image. It will be used only to measure minimum compression level required
     pub fn set_baseline(&self, image: Arc<PngImage>) {
-        self.try_image_inner(image, false)
+        self.try_image_inner(image, 1.0, false)
     }
 
     /// Check if the image is smaller than others
-    pub fn try_image(&self, image: Arc<PngImage>) {
-        self.try_image_inner(image, true)
+    /// Bias is a value in 0..=1 range. Compressed size is multiplied by
+    /// this fraction when comparing to the best, so 0.95 allows 5% larger size.
+    pub fn try_image(&self, image: Arc<PngImage>, bias: f32) {
+        self.try_image_inner(image, bias, true)
     }
 
-    fn try_image_inner(&self, image: Arc<PngImage>, is_reduction: bool) {
-        self.eval_send.as_ref().expect("not finished yet").send((image, is_reduction)).expect("send")
+    fn try_image_inner(&self, image: Arc<PngImage>, bias: f32, is_reduction: bool) {
+        self.eval_send.as_ref().expect("not finished yet").send((image, bias, is_reduction)).expect("send")
     }
 
     /// Main loop of evaluation thread
-    fn evaluate_images(from_channel: Receiver<(Arc<PngImage>, bool)>) -> Option<PngData> {
+    fn evaluate_images(from_channel: Receiver<(Arc<PngImage>, f32, bool)>) -> Option<PngData> {
         let best_candidate_size = AtomicMin::new(None);
         let best_result: Mutex<Option<(PngData, _, _)>> = Mutex::new(None);
         // ends when sender is dropped
-        for (nth, (image, is_reduction)) in from_channel.iter().enumerate() {
+        for (nth, (image, bias, is_reduction)) in from_channel.iter().enumerate() {
             #[cfg(feature = "parallel")]
             let filters_iter = STD_FILTERS.par_iter().with_max_len(1);
             #[cfg(not(feature = "parallel"))]
@@ -75,15 +77,16 @@ impl Evaluator {
                     &best_candidate_size,
                 ) {
                     let mut res = best_result.lock().unwrap();
-                    if best_candidate_size.get().map_or(true, |best_len| {
+                    if best_candidate_size.get().map_or(true, |old_best_len| {
+                        let new_len = (idat_data.len() as f64 * bias as f64) as usize;
                         // a tie-breaker is required to make evaluation deterministic
                         if let Some(res) = res.as_ref() {
                             // choose smallest compressed, or if compresses the same, smallest uncompressed, or cheaper filter
                             let old_img = &res.0.raw;
-                            let new = (idat_data.len(), image.data.len(), image.ihdr.bit_depth, f, nth);
-                            let old = (best_len, old_img.data.len(), old_img.ihdr.bit_depth, res.1, res.2);
+                            let new = (new_len, image.data.len(), image.ihdr.bit_depth, f, nth);
+                            let old = (old_best_len, old_img.data.len(), old_img.ihdr.bit_depth, res.1, res.2);
                             new < old
-                        } else if best_len > idat_data.len() {
+                        } else if new_len < old_best_len {
                             true
                         } else {
                             false
diff --git a/src/lib.rs b/src/lib.rs
index be18e74d..1a54cf82 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -747,7 +747,7 @@ fn perform_reductions(mut png: Arc<PngImage>, opts: &Options, deadline: &Deadlin
     if let Some(interlacing) = opts.interlace {
         if let Some(reduced) = png.change_interlacing(interlacing) {
             png = Arc::new(reduced);
-            eval.try_image(png.clone());
+            eval.try_image(png.clone(), 0.);
         }
         if deadline.passed() {
             return;
@@ -757,7 +757,7 @@ fn perform_reductions(mut png: Arc<PngImage>, opts: &Options, deadline: &Deadlin
     if opts.palette_reduction {
         if let Some(reduced) = reduced_palette(&png) {
             png = Arc::new(reduced);
-            eval.try_image(png.clone());
+            eval.try_image(png.clone(), 0.95);
             if opts.verbosity == Some(1) {
                 report_reduction(&png);
             }
@@ -772,11 +772,11 @@ fn perform_reductions(mut png: Arc<PngImage>, opts: &Options, deadline: &Deadlin
             let previous = png.clone();
             let bits = reduced.ihdr.bit_depth;
             png = Arc::new(reduced);
-            eval.try_image(png.clone());
+            eval.try_image(png.clone(), 1.0);
             if (bits == BitDepth::One || bits == BitDepth::Two) && previous.ihdr.bit_depth != BitDepth::Four {
                 // Also try 16-color mode for all lower bits images, since that may compress better
                 if let Some(reduced) = reduce_bit_depth(&previous, 4) {
-                    eval.try_image(Arc::new(reduced));
+                    eval.try_image(Arc::new(reduced), 0.98);
                 }
             }
             if opts.verbosity == Some(1) {
@@ -791,7 +791,7 @@ fn perform_reductions(mut png: Arc<PngImage>, opts: &Options, deadline: &Deadlin
     if opts.color_type_reduction {
         if let Some(reduced) = reduce_color_type(&png) {
             png = Arc::new(reduced);
-            eval.try_image(png.clone());
+            eval.try_image(png.clone(), 0.96);
             if opts.verbosity == Some(1) {
                 report_reduction(&png);
             }
diff --git a/src/reduction/alpha.rs b/src/reduction/alpha.rs
index b013ab23..e2bba245 100644
--- a/src/reduction/alpha.rs
+++ b/src/reduction/alpha.rs
@@ -19,7 +19,7 @@ pub fn try_alpha_reductions(png: Arc<PngImage>, alphas: &HashSet<AlphaOptim>, ev
     let alphas_iter = alphas.iter();
     alphas_iter
         .filter_map(|&alpha| filtered_alpha_channel(&png, *alpha))
-        .for_each(|image| eval.try_image(Arc::new(image)));
+        .for_each(|image| eval.try_image(Arc::new(image), 0.99));
 }
 
 pub fn filtered_alpha_channel(png: &PngImage, optim: AlphaOptim) -> Option<PngImage> {