diff --git a/src/PIL/IcoImagePlugin.py b/src/PIL/IcoImagePlugin.py
index 60855860a..ea3a35e74 100644
--- a/src/PIL/IcoImagePlugin.py
+++ b/src/PIL/IcoImagePlugin.py
@@ -142,11 +142,11 @@ class IcoFile:
             msg = "No images were found"
             raise TypeError(msg)
 
-        self.entry = sorted(self.entry, key=lambda x: x["color_depth"])
-        # ICO images are usually squares
-        # self.entry = sorted(self.entry, key=lambda x: x['width'])
-        self.entry = sorted(self.entry, key=lambda x: x["square"])
-        self.entry.reverse()
+        # Ensure self.entry is sorted by size and colorfulness, largest first
+        self.entry.sort(
+            key=lambda x: (x["width"] * x["height"], x["color_depth"]),
+            reverse=True,
+        )
 
     def _check_header(self, header):
         if not _accept(header):
@@ -181,8 +181,6 @@ class IcoFile:
             or (icon_header["nb_color"] != 0 and ceil(log(icon_header["nb_color"], 2)))
             or 256
         )
-        icon_header["dim"] = (icon_header["width"], icon_header["height"])
-        icon_header["square"] = icon_header["width"] * icon_header["height"]
         return icon_header
 
     def sizes(self):
@@ -191,9 +189,17 @@ class IcoFile:
         """
         return {(h["width"], h["height"]) for h in self.entry}
 
+    def largest_size(self):
+        """
+        Get the largest icon size.
+        """
+        return max(self.sizes(), key=lambda x: x[0] * x[1])
+
     def getentryindex(self, size, bpp=False):
         for i, h in enumerate(self.entry):
-            if size == h["dim"] and (bpp is False or bpp == h["color_depth"]):
+            if size == (h["width"], h["height"]) and (
+                bpp is False or bpp == h["color_depth"]
+            ):
                 return i
         return 0
 
@@ -317,7 +323,7 @@ class IcoImageFile(ImageFile.ImageFile):
     def _open(self):
         self.ico = self._ico_file_class(self.fp)
         self.info["sizes"] = self.ico.sizes()
-        self.size = self.ico.entry[0]["dim"]
+        self.size = self.ico.largest_size()
         self.load()
 
     @property