diff --git a/compiler/src/dotty/tools/dotc/core/Definitions.scala b/compiler/src/dotty/tools/dotc/core/Definitions.scala
index 4886bfe0eb32..c95201086200 100644
--- a/compiler/src/dotty/tools/dotc/core/Definitions.scala
+++ b/compiler/src/dotty/tools/dotc/core/Definitions.scala
@@ -153,10 +153,12 @@ class Definitions {
       tl => op(tl.paramRefs(0), tl.paramRefs(1))))
 
   private def enterPolyMethod(cls: ClassSymbol, name: TermName, typeParamCount: Int,
-                    resultTypeFn: PolyType => Type, flags: FlagSet = EmptyFlags,
+                    resultTypeFn: PolyType => Type,
+                    flags: FlagSet = EmptyFlags,
+                    bounds: TypeBounds = TypeBounds.empty,
                     useCompleter: Boolean = false) = {
     val tparamNames = PolyType.syntheticParamNames(typeParamCount)
-    val tparamInfos = tparamNames map (_ => TypeBounds.empty)
+    val tparamInfos = tparamNames map (_ => bounds)
     def ptype = PolyType(tparamNames)(_ => tparamInfos, resultTypeFn)
     val info =
       if (useCompleter)
@@ -244,36 +246,32 @@ class Definitions {
    *  - Have other methods exist only in Object.
    * To achieve this, we synthesize all Any and Object methods; Object methods no longer get
    * loaded from a classfile.
-   *
-   * There's a remaining question about `getClass`. In Scala2.x `getClass` was handled by compiler magic.
-   * This is deemed too cumersome for Dotty and therefore right now `getClass` gets no special treatment;
-   * it's just a method on `Any` which returns the raw type `java.lang.Class`. An alternative
-   * way to get better `getClass` typing would be to treat `getClass` as a method of a generic
-   * decorator which gets remapped in a later phase to Object#getClass. Then we could give it
-   * the right type without changing the typechecker:
-   *
-   *     implicit class AnyGetClass[T](val x: T) extends AnyVal {
-   *       def getClass: java.lang.Class[T] = ???
-   *     }
    */
   @tu lazy val AnyClass: ClassSymbol = completeClass(enterCompleteClassSymbol(ScalaPackageClass, tpnme.Any, Abstract, Nil), ensureCtor = false)
   def AnyType: TypeRef = AnyClass.typeRef
   @tu lazy val AnyValClass: ClassSymbol = completeClass(enterCompleteClassSymbol(ScalaPackageClass, tpnme.AnyVal, Abstract, List(AnyClass.typeRef)))
   def AnyValType: TypeRef = AnyValClass.typeRef
 
-    @tu lazy val Any_== : TermSymbol       = enterMethod(AnyClass, nme.EQ, methOfAny(BooleanType), Final)
-    @tu lazy val Any_!= : TermSymbol       = enterMethod(AnyClass, nme.NE, methOfAny(BooleanType), Final)
-    @tu lazy val Any_equals: TermSymbol   = enterMethod(AnyClass, nme.equals_, methOfAny(BooleanType))
-    @tu lazy val Any_hashCode: TermSymbol = enterMethod(AnyClass, nme.hashCode_, MethodType(Nil, IntType))
-    @tu lazy val Any_toString: TermSymbol = enterMethod(AnyClass, nme.toString_, MethodType(Nil, StringType))
-    @tu lazy val Any_## : TermSymbol       = enterMethod(AnyClass, nme.HASHHASH, ExprType(IntType), Final)
-    @tu lazy val Any_getClass: TermSymbol = enterMethod(AnyClass, nme.getClass_, MethodType(Nil, ClassClass.typeRef.appliedTo(TypeBounds.empty)), Final)
+    @tu lazy val Any_== : TermSymbol           = enterMethod(AnyClass, nme.EQ, methOfAny(BooleanType), Final)
+    @tu lazy val Any_!= : TermSymbol          = enterMethod(AnyClass, nme.NE, methOfAny(BooleanType), Final)
+    @tu lazy val Any_equals: TermSymbol       = enterMethod(AnyClass, nme.equals_, methOfAny(BooleanType))
+    @tu lazy val Any_hashCode: TermSymbol     = enterMethod(AnyClass, nme.hashCode_, MethodType(Nil, IntType))
+    @tu lazy val Any_toString: TermSymbol     = enterMethod(AnyClass, nme.toString_, MethodType(Nil, StringType))
+    @tu lazy val Any_## : TermSymbol          = enterMethod(AnyClass, nme.HASHHASH, ExprType(IntType), Final)
     @tu lazy val Any_isInstanceOf: TermSymbol = enterT1ParameterlessMethod(AnyClass, nme.isInstanceOf_, _ => BooleanType, Final)
     @tu lazy val Any_asInstanceOf: TermSymbol = enterT1ParameterlessMethod(AnyClass, nme.asInstanceOf_, _.paramRefs(0), Final)
-    @tu lazy val Any_typeTest: TermSymbol = enterT1ParameterlessMethod(AnyClass, nme.isInstanceOfPM, _ => BooleanType, Final | Synthetic | Artifact)
-    @tu lazy val Any_typeCast: TermSymbol = enterT1ParameterlessMethod(AnyClass, nme.asInstanceOfPM, _.paramRefs(0), Final | Synthetic | Artifact | StableRealizable)
+    @tu lazy val Any_typeTest: TermSymbol     = enterT1ParameterlessMethod(AnyClass, nme.isInstanceOfPM, _ => BooleanType, Final | Synthetic | Artifact)
+    @tu lazy val Any_typeCast: TermSymbol     = enterT1ParameterlessMethod(AnyClass, nme.asInstanceOfPM, _.paramRefs(0), Final | Synthetic | Artifact | StableRealizable)
       // generated by pattern matcher, eliminated by erasure
 
+    /** def getClass[A >: this.type](): Class[? <: A] */
+    @tu lazy val Any_getClass: TermSymbol =
+        enterPolyMethod(
+          AnyClass, nme.getClass_, 1,
+          pt => MethodType(Nil, ClassClass.typeRef.appliedTo(TypeBounds.upper(pt.paramRefs(0)))),
+          Final,
+          bounds = TypeBounds.lower(AnyClass.thisType))
+
     def AnyMethods: List[TermSymbol] = List(Any_==, Any_!=, Any_equals, Any_hashCode,
       Any_toString, Any_##, Any_getClass, Any_isInstanceOf, Any_asInstanceOf, Any_typeTest, Any_typeCast)
 
diff --git a/compiler/src/dotty/tools/dotc/transform/InterceptedMethods.scala b/compiler/src/dotty/tools/dotc/transform/InterceptedMethods.scala
index 5b3ba45e1850..be456b9b8e27 100644
--- a/compiler/src/dotty/tools/dotc/transform/InterceptedMethods.scala
+++ b/compiler/src/dotty/tools/dotc/transform/InterceptedMethods.scala
@@ -21,7 +21,6 @@ object InterceptedMethods {
   * - `x.##` for ## in NullClass becomes `0`
   * - `x.##` for ## in Any becomes calls to ScalaRunTime.hash,
   *     using the most precise overload available
-  * - `x.getClass` for getClass in primitives becomes `x.getClass` with getClass in class Object.
   */
 class InterceptedMethods extends MiniPhase {
   import tpd._
@@ -62,11 +61,6 @@ class InterceptedMethods extends MiniPhase {
   }
 
   override def transformApply(tree: Apply)(implicit ctx: Context): Tree = {
-    def unknown = {
-      assert(false, s"The symbol '${tree.fun.symbol.showLocated}' was intercepted but didn't match any cases, " +
-        s"that means the intercepted methods set doesn't match the code")
-      tree
-    }
     lazy val qual = tree.fun match {
       case Select(qual, _) => qual
       case ident @ Ident(_) =>
@@ -78,32 +72,9 @@ class InterceptedMethods extends MiniPhase {
         }
     }
 
-    val Any_!= = defn.Any_!=
-    val rewritten: Tree = tree.fun.symbol match {
-      case Any_!= =>
-        qual.select(defn.Any_==).appliedToArgs(tree.args).select(defn.Boolean_!).withSpan(tree.span)
-        /*
-        /* else if (isPrimitiveValueClass(qual.tpe.typeSymbol)) {
-            // todo: this is needed to support value classes
-            // Rewrite 5.getClass to ScalaRunTime.anyValClass(5)
-            global.typer.typed(gen.mkRuntimeCall(nme.anyValClass,
-              List(qual, typer.resolveClassTag(tree.pos, qual.tpe.widen))))
-          }*/
-         */
-      case t if t.name == nme.getClass_ && defn.ScalaValueClasses().contains(t.owner) =>
-          // if we got here then we're trying to send a primitive getClass method to either
-          // a) an Any, in which cage Object_getClass works because Any erases to object. Or
-          //
-          // b) a non-primitive, e.g. because the qualifier's type is a refinement type where one parent
-          //    of the refinement is a primitive and another is AnyRef. In that case
-          //    we get a primitive form of _getClass trying to target a boxed value
-          //    so we need replace that method name with Object_getClass to get correct behavior.
-          //    See SI-5568.
-        qual.selectWithSig(defn.Any_getClass).appliedToNone.withSpan(tree.span)
-      case _ =>
-        tree
-    }
-    ctx.log(s"$phaseName rewrote $tree to $rewritten")
-    rewritten
+    if tree.fun.symbol == defn.Any_!= then
+      qual.select(defn.Any_==).appliedToArgs(tree.args).select(defn.Boolean_!).withSpan(tree.span)
+    else
+      tree
   }
 }
diff --git a/compiler/test-resources/repl/getClass b/compiler/test-resources/repl/getClass
index 7b3d0bcedd09..6591129a0be9 100644
--- a/compiler/test-resources/repl/getClass
+++ b/compiler/test-resources/repl/getClass
@@ -1,4 +1,5 @@
 scala> val xs = List(1)
 val xs: List[Int] = List(1)
 scala> xs.getClass
-val res0: Class[?] = class scala.collection.immutable.$colon$colon
+val res0: Class[? <: List[Int]] = class scala.collection.immutable.$colon$colon
+
diff --git a/tests/pending/run/t5568.check b/tests/pending/run/t5568.check
deleted file mode 100644
index 67aaf16e079f..000000000000
--- a/tests/pending/run/t5568.check
+++ /dev/null
@@ -1,9 +0,0 @@
-void
-int
-class scala.runtime.BoxedUnit
-class scala.runtime.BoxedUnit
-class java.lang.Integer
-class java.lang.Integer
-5
-5
-5
diff --git a/tests/pending/run/t5568.flags b/tests/pending/run/t5568.flags
deleted file mode 100644
index ad51758c3932..000000000000
--- a/tests/pending/run/t5568.flags
+++ /dev/null
@@ -1 +0,0 @@
--nowarn
diff --git a/tests/pos/i3495.scala b/tests/pos/i3495.scala
new file mode 100644
index 000000000000..e77bcc5e1630
--- /dev/null
+++ b/tests/pos/i3495.scala
@@ -0,0 +1,13 @@
+class A
+
+object Test {
+  val x: A = new A()
+
+  def y = x.getClass
+
+  val z: Class[? <: A] = y
+
+  1.getClass
+
+}
+
diff --git a/tests/pos/t1107b/T.scala b/tests/pos/t1107b/T.scala
index 0dff0b94fdc3..5889d43548a0 100644
--- a/tests/pos/t1107b/T.scala
+++ b/tests/pos/t1107b/T.scala
@@ -2,6 +2,6 @@ sealed trait Top
 sealed trait Sub extends Top
 trait C {
   private object P extends Sub
-  def bob() = P.getClass
+  def bob(): Class[_] = P.getClass
   def bob2() = O.d(P)
 }
diff --git a/tests/run/t5568.check b/tests/run/t5568.check
new file mode 100644
index 000000000000..90c75aafaa43
--- /dev/null
+++ b/tests/run/t5568.check
@@ -0,0 +1,9 @@
+void
+int
+void
+void
+int
+int
+5
+5
+5
diff --git a/tests/pending/run/t5568.scala b/tests/run/t5568.scala
similarity index 100%
rename from tests/pending/run/t5568.scala
rename to tests/run/t5568.scala