diff --git a/compiler/src/dotty/tools/dotc/typer/ProtoTypes.scala b/compiler/src/dotty/tools/dotc/typer/ProtoTypes.scala
index 9f83157981b5..43b035bcedfa 100644
--- a/compiler/src/dotty/tools/dotc/typer/ProtoTypes.scala
+++ b/compiler/src/dotty/tools/dotc/typer/ProtoTypes.scala
@@ -222,7 +222,9 @@ object ProtoTypes {
   class UnapplySelectionProto(name: Name) extends SelectionProto(name, WildcardType, NoViewsAllowed, true)
 
   trait ApplyingProto extends ProtoType   // common trait of ViewProto and FunProto
-  trait FunOrPolyProto extends ProtoType  // common trait of PolyProto and FunProto
+  trait FunOrPolyProto extends ProtoType { // common trait of PolyProto and FunProto
+    def isGivenApply: Boolean = false
+  }
 
   class FunProtoState {
 
@@ -244,7 +246,7 @@ object ProtoTypes {
    *  [](args): resultType
    */
   case class FunProto(args: List[untpd.Tree], resType: Type)(typer: Typer,
-    val isGivenApply: Boolean, state: FunProtoState = new FunProtoState)(implicit val ctx: Context)
+    override val isGivenApply: Boolean, state: FunProtoState = new FunProtoState)(implicit val ctx: Context)
   extends UncachedGroundType with ApplyingProto with FunOrPolyProto {
     override def resultType(implicit ctx: Context): Type = resType
 
diff --git a/compiler/src/dotty/tools/dotc/typer/Typer.scala b/compiler/src/dotty/tools/dotc/typer/Typer.scala
index 00289794ee73..bbe69402fcd1 100644
--- a/compiler/src/dotty/tools/dotc/typer/Typer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Typer.scala
@@ -2421,18 +2421,26 @@ class Typer extends Namer
         case alt :: Nil =>
           readaptSimplified(tree.withType(alt))
         case Nil =>
+          // If alternative matches, there are still two ways to recover:
+          //  1. If context is an application, try to insert an apply or implicit
+          //  2. If context is not an application, pick a alternative that does
+          //     not take parameters.
           def noMatches =
             errorTree(tree, NoMatchingOverload(altDenots, pt)(err))
           def hasEmptyParams(denot: SingleDenotation) = denot.info.paramInfoss == ListOfNil
           pt match {
-            case pt: FunProto if !pt.isGivenApply =>
-              // insert apply or convert qualifier only for a regular application
+            case pt: FunOrPolyProto if !pt.isGivenApply =>
+              // insert apply or convert qualifier, but only for a regular application
               tryInsertApplyOrImplicit(tree, pt, locked)(noMatches)
             case _ =>
-              if (altDenots exists (_.info.paramInfoss == ListOfNil))
-                typed(untpd.Apply(untpd.TypedSplice(tree), Nil), pt, locked)
-              else
-                noMatches
+              alts.filter(_.info.isParameterless) match {
+                case alt :: Nil => readaptSimplified(tree.withType(alt))
+                case _ =>
+                  if (altDenots exists (_.info.paramInfoss == ListOfNil))
+                    typed(untpd.Apply(untpd.TypedSplice(tree), Nil), pt, locked)
+                  else
+                    noMatches
+              }
           }
         case alts =>
           if (tree.tpe.isErroneous || pt.isErroneous) tree.withType(UnspecifiedErrorType)
diff --git a/tests/pos/i6705.scala b/tests/pos/i6705.scala
new file mode 100644
index 000000000000..40ad62cf1713
--- /dev/null
+++ b/tests/pos/i6705.scala
@@ -0,0 +1,14 @@
+trait StringTempl {
+  def mkString: String
+  def mkString(x: String): String
+}
+
+
+object Test {
+  def (x: String) shouldBe(y: String): Boolean = ???
+
+  def test(tmpl: StringTempl): Unit = {
+    tmpl.mkString shouldBe "hello"                       // error
+    tmpl.mkString(", world") shouldBe "hello, world"
+  }
+}
\ No newline at end of file