diff --git a/Dapper/DefaultTypeMap.cs b/Dapper/DefaultTypeMap.cs
index b278250cb..12e431522 100644
--- a/Dapper/DefaultTypeMap.cs
+++ b/Dapper/DefaultTypeMap.cs
@@ -74,8 +74,16 @@ public ConstructorInfo FindConstructor(string[] names, Type[] types)
                 int i = 0;
                 for (; i < ctorParameters.Length; i++)
                 {
-                    if (!string.Equals(ctorParameters[i].Name, names[i], StringComparison.OrdinalIgnoreCase))
+                    if (EqualsCI(ctorParameters[i].Name, names[i]))
+                    { } // exact match
+                    else if (MatchNamesWithUnderscores && EqualsCIU(ctorParameters[i].Name, names[i]))
+                    { } // match after applying underscores
+                    else
+                    {
+                        // not a name match
                         break;
+                    }
+
                     if (types[i] == typeof(byte[]) && ctorParameters[i].ParameterType.FullName == SqlMapper.LinqBinary)
                         continue;
                     var unboxedType = Nullable.GetUnderlyingType(ctorParameters[i].ParameterType) ?? ctorParameters[i].ParameterType;
@@ -119,9 +127,8 @@ public ConstructorInfo FindExplicitConstructor()
         /// <returns>Mapping implementation</returns>
         public SqlMapper.IMemberMap GetConstructorParameter(ConstructorInfo constructor, string columnName)
         {
-            var parameters = constructor.GetParameters();
-
-            return new SimpleMemberMap(columnName, parameters.FirstOrDefault(p => string.Equals(p.Name, columnName, StringComparison.OrdinalIgnoreCase)));
+            ParameterInfo param = MatchFirstOrDefault(constructor.GetParameters(), columnName, static p => p.Name);
+            return new SimpleMemberMap(columnName, param);
         }
 
         /// <summary>
@@ -131,14 +138,7 @@ public SqlMapper.IMemberMap GetConstructorParameter(ConstructorInfo constructor,
         /// <returns>Mapping implementation</returns>
         public SqlMapper.IMemberMap GetMember(string columnName)
         {
-            var property = Properties.Find(p => string.Equals(p.Name, columnName, StringComparison.Ordinal))
-               ?? Properties.Find(p => string.Equals(p.Name, columnName, StringComparison.OrdinalIgnoreCase));
-
-            if (property == null && MatchNamesWithUnderscores)
-            {
-                property = Properties.Find(p => string.Equals(p.Name, columnName.Replace("_", ""), StringComparison.Ordinal))
-                    ?? Properties.Find(p => string.Equals(p.Name, columnName.Replace("_", ""), StringComparison.OrdinalIgnoreCase));
-            }
+            var property = MatchFirstOrDefault(Properties, columnName, static p => p.Name);
 
             if (property != null)
                 return new SimpleMemberMap(columnName, property);
@@ -174,6 +174,54 @@ public SqlMapper.IMemberMap GetMember(string columnName)
         /// </summary>
         public static bool MatchNamesWithUnderscores { get; set; }
 
+        static T MatchFirstOrDefault<T>(IList<T> members, string name, Func<T, string> selector) where T : class
+        {
+            if (members is { Count: > 0 })
+            {
+                // try exact first
+                foreach (var member in members)
+                {
+                    if (string.Equals(name, selector(member), StringComparison.Ordinal))
+                    {
+                        return member;
+                    }
+                }
+                // then exact ignoring case
+                foreach (var member in members)
+                {
+                    if (string.Equals(name, selector(member), StringComparison.OrdinalIgnoreCase))
+                    {
+                        return member;
+                    }
+                }
+                if (MatchNamesWithUnderscores)
+                {
+                    // same again, minus underscore delta
+                    name = name?.Replace("_", "");
+                    foreach (var member in members)
+                    {
+                        if (string.Equals(name, selector(member)?.Replace("_", ""), StringComparison.Ordinal))
+                        {
+                            return member;
+                        }
+                    }
+                    foreach (var member in members)
+                    {
+                        if (string.Equals(name, selector(member)?.Replace("_", ""), StringComparison.OrdinalIgnoreCase))
+                        {
+                            return member;
+                        }
+                    }
+                }
+            }
+            return null;
+        }
+
+        internal static bool EqualsCI(string x, string y)
+            => string.Equals(x, y, StringComparison.OrdinalIgnoreCase);
+        internal static bool EqualsCIU(string x, string y)
+            => string.Equals(x?.Replace("_", ""), y?.Replace("_", ""), StringComparison.OrdinalIgnoreCase);
+
         /// <summary>
         /// The settable properties for this typemap
         /// </summary>
diff --git a/docs/index.md b/docs/index.md
index e2092effc..326c30cc8 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -22,6 +22,8 @@ Note: to get the latest pre-release build, add ` -Pre` to the end of the command
 
 ### unreleased
 
+- add underscore handling with constructors (#1786 via @jo-goro, fixes #818; also #1947 via mgravell)
+
 (note: new PRs will not be merged until they add release note wording here)
 
 ### 2.0.143
diff --git a/tests/Dapper.Tests/ConstructorTests.cs b/tests/Dapper.Tests/ConstructorTests.cs
index 4c72894ee..af8ae7afa 100644
--- a/tests/Dapper.Tests/ConstructorTests.cs
+++ b/tests/Dapper.Tests/ConstructorTests.cs
@@ -220,5 +220,45 @@ public void TestWithNonPublicConstructor()
             var output = connection.Query<WithPrivateConstructor>("select 1 as Foo").First();
             Assert.Equal(1, output.Foo);
         }
+
+        [Fact]
+        public void CtorWithUnderscores()
+        {
+            var obj = connection.QueryFirst<Type_ParamsWithUnderscores>("select 'abc' as FIRST_NAME, 'def' as LAST_NAME");
+            Assert.NotNull(obj);
+            Assert.Equal("abc", obj.FirstName);
+            Assert.Equal("def", obj.LastName);
+        }
+
+        [Fact]
+        public void CtorWithoutUnderscores()
+        {
+            DefaultTypeMap.MatchNamesWithUnderscores = true;
+            var obj = connection.QueryFirst<Type_ParamsWithoutUnderscores>("select 'abc' as FIRST_NAME, 'def' as LAST_NAME");
+            Assert.NotNull(obj);
+            Assert.Equal("abc", obj.FirstName);
+            Assert.Equal("def", obj.LastName);
+        }
+
+        class Type_ParamsWithUnderscores
+        {
+            public string FirstName { get; }
+            public string LastName { get; }
+            public Type_ParamsWithUnderscores(string first_name, string last_name)
+            {
+                FirstName = first_name;
+                LastName = last_name;
+            }
+        }
+        class Type_ParamsWithoutUnderscores
+        {
+            public string FirstName { get; }
+            public string LastName { get; }
+            public Type_ParamsWithoutUnderscores(string firstName, string lastName)
+            {
+                FirstName = firstName;
+                LastName = lastName;
+            }
+        }
     }
 }
diff --git a/tests/Dapper.Tests/MiscTests.cs b/tests/Dapper.Tests/MiscTests.cs
index 4d5dd26c4..608607a0d 100644
--- a/tests/Dapper.Tests/MiscTests.cs
+++ b/tests/Dapper.Tests/MiscTests.cs
@@ -1273,5 +1273,26 @@ private class HazGetOnly
             public int Id { get; }
             public string Name { get; } = "abc";
         }
+
+        [Fact]
+        public void TestConstructorParametersWithUnderscoredColumns()
+        {
+            DefaultTypeMap.MatchNamesWithUnderscores = true;
+            var obj = connection.QuerySingle<HazGetOnlyAndCtor>("select 42 as [id_property], 'def' as [name_property];");
+            Assert.Equal(42, obj.IdProperty);
+            Assert.Equal("def", obj.NameProperty);
+        }
+
+        private class HazGetOnlyAndCtor
+        {
+            public int IdProperty { get; }
+            public string NameProperty { get; }
+
+            public HazGetOnlyAndCtor(int idProperty, string nameProperty)
+            {
+                IdProperty = idProperty;
+                NameProperty = nameProperty;
+            }
+        }
     }
 }