diff --git a/compiler/src/dotty/tools/dotc/typer/Applications.scala b/compiler/src/dotty/tools/dotc/typer/Applications.scala
index 43154022e3a0..0e8b049fa59e 100644
--- a/compiler/src/dotty/tools/dotc/typer/Applications.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Applications.scala
@@ -1939,12 +1939,12 @@ trait Applications extends Compatibility {
 
         record("resolveOverloaded.FunProto", alts.length)
         val alts1 = narrowBySize(alts)
-        //report.log(i"narrowed by size: ${alts1.map(_.symbol.showDcl)}%, %")
+        overload.println(i"narrowed by size: ${alts1.map(_.symbol.showDcl)}%, %")
         if isDetermined(alts1) then alts1
         else
           record("resolveOverloaded.narrowedBySize", alts1.length)
           val alts2 = narrowByShapes(alts1)
-          //report.log(i"narrowed by shape: ${alts2.map(_.symbol.showDcl)}%, %")
+          overload.println(i"narrowed by shape: ${alts2.map(_.symbol.showDcl)}%, %")
           if isDetermined(alts2) then alts2
           else
             record("resolveOverloaded.narrowedByShape", alts2.length)
@@ -1977,8 +1977,14 @@ trait Applications extends Compatibility {
            *   new java.io.ObjectOutputStream(f)
            */
           pt match {
-            case SAMType(mtp) => narrowByTypes(alts, mtp.paramInfos, mtp.resultType)
-            case _ => compat
+            case SAMType(mtp) =>
+              narrowByTypes(alts, mtp.paramInfos, mtp.resultType)
+            case _ =>
+              // pick any alternatives that are not methods since these might be convertible
+              // to the expected type, or be used as extension method arguments.
+              val convertible = alts.filterNot(alt =>
+                  normalize(alt, IgnoredProto(pt)).widenSingleton.isInstanceOf[MethodType])
+              if convertible.length == 1 then convertible else compat
           }
         else compat
     }
diff --git a/tests/pos/i14729.scala b/tests/pos/i14729.scala
new file mode 100644
index 000000000000..03bb4038aa85
--- /dev/null
+++ b/tests/pos/i14729.scala
@@ -0,0 +1,19 @@
+class Foo():
+  def normal: Unit = println("normal")
+
+extension (f: Foo)
+  def ext: Unit = println("ext")
+
+object Bar:
+  def makeFoo[A]: Foo = Foo()
+  def makeFoo[A](s: String): Foo = Foo()
+
+def tests: Unit =
+  Bar.makeFoo[Int].ext // error
+
+  (Bar.makeFoo[Int]).ext // error
+
+  val foo = Bar.makeFoo[Int]
+  foo.ext // ok
+
+  Bar.makeFoo[Int].normal // ok