diff --git a/src/runtime/converter.cs b/src/runtime/converter.cs
index 420fc9435..dd8598e33 100644
--- a/src/runtime/converter.cs
+++ b/src/runtime/converter.cs
@@ -29,6 +29,8 @@ private Converter()
         private static Type int64Type;
         private static Type boolType;
         private static Type typeType;
+        private static Type uint64Type;
+        private static Type uint32Type;
 
         static Converter()
         {
@@ -43,13 +45,15 @@ static Converter()
             decimalType = typeof(Decimal);
             boolType = typeof(Boolean);
             typeType = typeof(Type);
+            uint64Type = typeof(UInt64);
+            uint32Type = typeof(UInt32);
         }
 
 
         /// <summary>
         /// Given a builtin Python type, return the corresponding CLR type.
         /// </summary>
-        internal static Type GetTypeByAlias(IntPtr op)
+        internal static Type GetTypeByAlias(IntPtr op, Type preferred=null)
         {
             if (op == Runtime.PyStringType)
                 return stringType;
@@ -57,12 +61,18 @@ internal static Type GetTypeByAlias(IntPtr op)
             if (op == Runtime.PyUnicodeType)
                 return stringType;
 
-            if (op == Runtime.PyIntType)
+            if (op == Runtime.PyIntType && (preferred == null || preferred == int32Type))
                 return int32Type;
 
-            if (op == Runtime.PyLongType)
+            if (op == Runtime.PyIntType && (preferred == null || preferred == uint32Type))
+                return uint32Type;
+
+            if (op == Runtime.PyLongType && (preferred == null || preferred == int64Type))
                 return int64Type;
 
+            if (op == Runtime.PyLongType && (preferred == null || preferred == uint64Type))
+                return uint64Type;
+
             if (op == Runtime.PyFloatType)
                 return doubleType;
 
diff --git a/src/runtime/methodbinder.cs b/src/runtime/methodbinder.cs
index 1b7cc4736..b72e3d963 100644
--- a/src/runtime/methodbinder.cs
+++ b/src/runtime/methodbinder.cs
@@ -330,6 +330,7 @@ public MatchedMethod(int kwargsMatched, int defaultsNeeded, object[] margs, int
                 ManagedArgs = margs;
                 Outs = outs;
                 Method = mb;
+                HasPyObjectParameter = mb.GetParameters().Any(x => x.ParameterType == typeof(PyObject));
             }
 
             public int KwargsMatched { get; }
@@ -337,6 +338,7 @@ public MatchedMethod(int kwargsMatched, int defaultsNeeded, object[] margs, int
             public object[] ManagedArgs { get; }
             public int Outs { get; }
             public MethodBase Method { get; }
+            public bool HasPyObjectParameter { get; }
         }
 
         private readonly struct MismatchedMethod
@@ -470,8 +472,15 @@ internal Binding Bind(IntPtr inst, IntPtr args, IntPtr kw, MethodBase info, Meth
                 var matchedMethod = new MatchedMethod(kwargsMatched, defaultsNeeded, margs, outs, mi);
                 argMatchedMethods.Add(matchedMethod);
             }
+
             if (argMatchedMethods.Count > 0)
             {
+                // order the matched methods such that PyObject overrides are last, we only care about
+                // this when there is more than one arg matched method
+                if (argMatchedMethods.Count > 1)
+                {
+                    argMatchedMethods = argMatchedMethods.OrderBy(x => x.HasPyObjectParameter).ToList();
+                }
                 var bestKwargMatchCount = argMatchedMethods.Max(x => x.KwargsMatched);
                 var fewestDefaultsRequired = argMatchedMethods.Where(x => x.KwargsMatched == bestKwargMatchCount).Min(x => x.DefaultsNeeded);
 
@@ -725,7 +734,7 @@ static Type TryComputeClrArgumentType(Type parameterType, IntPtr argument, bool
                 pyoptype = Runtime.PyObject_Type(argument);
                 if (pyoptype != IntPtr.Zero)
                 {
-                    clrtype = Converter.GetTypeByAlias(pyoptype);
+                    clrtype = Converter.GetTypeByAlias(pyoptype, parameterType);
                 }
                 Runtime.XDecref(pyoptype);
             }
diff --git a/src/testing/conversiontest.cs b/src/testing/conversiontest.cs
index 1f9d64e1b..f67551bb7 100644
--- a/src/testing/conversiontest.cs
+++ b/src/testing/conversiontest.cs
@@ -42,7 +42,7 @@ public ConversionTest()
 
     }
 
-    
+
 
     public interface ISpam
     {
@@ -63,7 +63,7 @@ public string GetValue()
             return value;
         }
     }
-    
+
     public class UnicodeString
     {
         public string value = "안녕";
@@ -78,4 +78,17 @@ public override string ToString()
             return value;
         }
     }
+
+    public class MethodResolutionInt
+    {
+        public IEnumerable<byte> MethodA(ulong address, int size)
+        {
+            return new byte[10];
+        }
+
+        public int MethodA(string dummy, ulong address, int size)
+        {
+            return 0;
+        }
+    }
 }
diff --git a/tests/test_conversion.py b/tests/test_conversion.py
index eec2bcde6..8fa972a3e 100644
--- a/tests/test_conversion.py
+++ b/tests/test_conversion.py
@@ -4,7 +4,7 @@
 import pytest
 
 import System
-from Python.Test import ConversionTest, UnicodeString
+from Python.Test import ConversionTest, UnicodeString, MethodResolutionInt
 from Python.Runtime import PyObjectConversions
 from Python.Runtime.Codecs import RawProxyEncoder
 
@@ -681,3 +681,15 @@ def CanEncode(self, clr_type):
     l = ob.ListField
     l.Add(42)
     assert ob.ListField.Count == 1
+
+def test_int_param_resolution_required():
+    """Test resolution of `int` parameters when resolution is needed"""
+
+    mri = MethodResolutionInt()
+    data = list(mri.MethodA(0x1000, 10))
+    assert len(data) == 10
+    assert data[0] == 0
+
+    data = list(mri.MethodA(0x100000000, 10))
+    assert len(data) == 10
+    assert data[0] == 0