diff --git a/compiler/src/dotty/tools/dotc/core/TypeApplications.scala b/compiler/src/dotty/tools/dotc/core/TypeApplications.scala
index dfbeef4e2ddc..fb2300ff1829 100644
--- a/compiler/src/dotty/tools/dotc/core/TypeApplications.scala
+++ b/compiler/src/dotty/tools/dotc/core/TypeApplications.scala
@@ -268,6 +268,19 @@ class TypeApplications(val self: Type) extends AnyVal {
     case _ => NoType
   }
 
+  /** Do self and other have the same kinds (not counting bounds and variances) */
+  def hasSameKindAs(other: Type)(implicit ctx: Context): Boolean = {
+    // println(i"check kind $self $other") // DEBUG
+    val selfResult = self.hkResult
+    val otherResult = other.hkResult
+    if (selfResult.exists)
+      otherResult.exists &&
+      selfResult.hasSameKindAs(otherResult) &&
+      self.typeParams.corresponds(other.typeParams)((sparam, oparam) =>
+        sparam.paramInfo.hasSameKindAs(oparam.paramInfo))
+    else !otherResult.exists
+  }
+
   /** Dealias type if it can be done without forcing the TypeRef's info */
   def safeDealias(implicit ctx: Context): Type = self match {
     case self: TypeRef if self.denot.exists && self.symbol.isAliasType =>
diff --git a/compiler/src/dotty/tools/dotc/typer/Checking.scala b/compiler/src/dotty/tools/dotc/typer/Checking.scala
index 39faed0412ee..72ce89a33942 100644
--- a/compiler/src/dotty/tools/dotc/typer/Checking.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Checking.scala
@@ -109,26 +109,9 @@ object Checking {
    *  types. Self application needs to be avoided since it can lead to stack overflows.
    *  Test cases are neg/i2771.scala and neg/i2771b.scala.
    */
-  def preCheckKind(arg: Tree, paramBounds: TypeBounds)(implicit ctx: Context): Tree = {
-    def result(tp: Type): Type = tp match {
-      case tp: HKTypeLambda => tp.resultType
-      case tp: TypeProxy => result(tp.superType)
-      case _ => defn.AnyType
-    }
-    def kindOK(argType: Type, boundType: Type): Boolean = {
-      // println(i"check kind rank2$arg $argType $boundType") // DEBUG
-      val argResult = argType.hkResult
-      val boundResult = argType.hkResult
-      if (argResult.exists)
-        boundResult.exists &&
-        kindOK(boundResult, argResult) &&
-        argType.typeParams.corresponds(boundType.typeParams)((ap, bp) =>
-          kindOK(ap.paramInfo, bp.paramInfo))
-      else !boundResult.exists
-    }
-    if (kindOK(arg.tpe, paramBounds.hi)) arg
-    else errorTree(arg, em"${arg.tpe} has wrong kind")
-  }
+  def preCheckKind(arg: Tree, paramBounds: TypeBounds)(implicit ctx: Context): Tree =
+    if (arg.tpe.widen.isRef(defn.NothingClass) || arg.tpe.hasSameKindAs(paramBounds.hi)) arg
+    else errorTree(arg, em"Type argument ${arg.tpe} has not the same kind as its bound $paramBounds")
 
   def preCheckKinds(args: List[Tree], paramBoundss: List[TypeBounds])(implicit ctx: Context): List[Tree] = {
     val args1 = args.zipWithConserve(paramBoundss)(preCheckKind)
diff --git a/compiler/src/dotty/tools/dotc/typer/RefChecks.scala b/compiler/src/dotty/tools/dotc/typer/RefChecks.scala
index 8f95eda31a4b..97d50b07e34e 100644
--- a/compiler/src/dotty/tools/dotc/typer/RefChecks.scala
+++ b/compiler/src/dotty/tools/dotc/typer/RefChecks.scala
@@ -183,25 +183,27 @@ object RefChecks {
     def infoString0(sym: Symbol, showLocation: Boolean) = {
       val sym1 = sym.underlyingSymbol
       def info = self.memberInfo(sym1)
-      i"${if (showLocation) sym1.showLocated else sym1}${
+      val infoStr =
         if (sym1.isAliasType) i", which equals ${info.bounds.hi}"
         else if (sym1.isAbstractType) i" with bounds$info"
         else if (sym1.is(Module)) ""
         else if (sym1.isTerm) i" of type $info"
         else ""
-      }"
+      i"${if (showLocation) sym1.showLocated else sym1}$infoStr"
     }
 
     /* Check that all conditions for overriding `other` by `member`
        * of class `clazz` are met.
        */
     def checkOverride(member: Symbol, other: Symbol): Unit = {
-      def memberTp = self.memberInfo(member)
-      def otherTp = self.memberInfo(other)
+      def memberTp(self: Type) =
+        if (member.isClass) TypeAlias(member.typeRef.EtaExpand(member.typeParams))
+        else self.memberInfo(member)
+      def otherTp(self: Type) = self.memberInfo(other)
 
       ctx.debuglog("Checking validity of %s overriding %s".format(member.showLocated, other.showLocated))
 
-      def noErrorType = !memberTp.isErroneous && !otherTp.isErroneous
+      def noErrorType = !memberTp(self).isErroneous && !otherTp(self).isErroneous
 
       def overrideErrorMsg(msg: String): String = {
         val isConcreteOverAbstract =
@@ -212,10 +214,10 @@ object RefChecks {
               infoStringWithLocation(other),
               infoStringWithLocation(member))
           else if (ctx.settings.debug.value)
-            err.typeMismatchMsg(memberTp, otherTp)
+            err.typeMismatchMsg(memberTp(self), otherTp(self))
           else ""
 
-        "overriding %s;\n %s %s%s".format(
+        "error overriding %s;\n %s %s%s".format(
           infoStringWithLocation(other), infoString(member), msg, addendum)
       }
 
@@ -248,13 +250,16 @@ object RefChecks {
 
       def compatibleTypes(memberTp: Type, otherTp: Type): Boolean =
         try
-          if (member.isType) { // intersection of bounds to refined types must be nonempty
+          if (member.isType) // intersection of bounds to refined types must be nonempty
             member.is(BaseTypeArg) ||
-            (memberTp frozen_<:< otherTp) || {
-              val jointBounds = (memberTp.bounds & otherTp.bounds).bounds
-              jointBounds.lo frozen_<:< jointBounds.hi
-            }
-          }
+            memberTp.bounds.hi.hasSameKindAs(otherTp.bounds.hi) &&
+            ((memberTp frozen_<:< otherTp) ||
+             !member.owner.derivesFrom(other.owner) && {
+               // if member and other come from independent classes or traits, their
+               // bounds must have non-empty-intersection
+               val jointBounds = (memberTp.bounds & otherTp.bounds).bounds
+               jointBounds.lo frozen_<:< jointBounds.hi
+             })
           else
             member.name.is(DefaultGetterName) || // default getters are not checked for compatibility
             memberTp.overrides(otherTp,
@@ -367,9 +372,9 @@ object RefChecks {
         overrideError("cannot be used here - term macros cannot override abstract methods")
       } else if (other.is(Macro) && !member.is(Macro)) { // (1.10)
         overrideError("cannot be used here - only term macros can override term macros")
-      } else if (!compatibleTypes(memberTp, otherTp) &&
-                 !compatibleTypes(upwardsSelf.memberInfo(member), upwardsSelf.memberInfo(other))) {
-        overrideError("has incompatible type" + err.whyNoMatchStr(memberTp, otherTp))
+      } else if (!compatibleTypes(memberTp(self), otherTp(self)) &&
+                 !compatibleTypes(memberTp(upwardsSelf), otherTp(upwardsSelf))) {
+        overrideError("has incompatible type" + err.whyNoMatchStr(memberTp(self), otherTp(self)))
       } else {
         checkOverrideDeprecated()
       }
diff --git a/compiler/src/dotty/tools/dotc/typer/Typer.scala b/compiler/src/dotty/tools/dotc/typer/Typer.scala
index cb73d37d34e5..2c8600e1c30e 100644
--- a/compiler/src/dotty/tools/dotc/typer/Typer.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Typer.scala
@@ -1131,8 +1131,7 @@ class Typer extends Namer with TypeAssigner with Applications with Implicits wit
           if (tpt1.symbol.isClass)
             tparam match {
               case tparam: Symbol =>
-                // This is needed to get the test `compileParSetSubset` to work
-                tparam.ensureCompleted()
+                tparam.ensureCompleted() // This is needed to get the test `compileParSetSubset` to work
               case _ =>
             }
           if (desugaredArg.isType) typed(desugaredArg, argPt)
@@ -1140,7 +1139,15 @@ class Typer extends Namer with TypeAssigner with Applications with Implicits wit
         }
         args.zipWithConserve(tparams)(typedArg(_, _)).asInstanceOf[List[Tree]]
       }
-      val args2 = preCheckKinds(args1, tparams.map(_.paramInfo.bounds))
+      val paramBounds = (tparams, args).zipped.map {
+        case (tparam, TypeBoundsTree(EmptyTree, EmptyTree)) =>
+          // if type argument is a wildcard, suppress kind checking since
+          // there is no real argument.
+          TypeBounds.empty
+        case (tparam, _) =>
+          tparam.paramInfo.bounds
+      }
+      val args2 = preCheckKinds(args1, paramBounds)
       // check that arguments conform to bounds is done in phase PostTyper
       assignType(cpy.AppliedTypeTree(tree)(tpt1, args2), tpt1, args2)
     }
diff --git a/tests/neg/i2770.scala b/tests/neg/i2770.scala
new file mode 100644
index 000000000000..4e7c6cb0a8cd
--- /dev/null
+++ b/tests/neg/i2770.scala
@@ -0,0 +1,14 @@
+trait A { type L }
+trait B extends A { type L[X] } // error: illegal override
+
+trait A2 { type L <: String }
+trait B2 extends A2 { type L[X] <: String } // error: illegal override
+trait C2 extends B2 { type L[X, Y] <: String } // error: illegal override
+
+trait D { type I }
+trait E extends D { type I <: String }
+trait F extends D { type I >: String }
+trait G extends E with F // ok
+
+trait H extends D { type I >: Int }
+trait H2 extends E with H // error: illegal override
diff --git a/tests/neg/i2771.scala b/tests/neg/i2771.scala
index 500f77919d23..838da3eaf9dc 100644
--- a/tests/neg/i2771.scala
+++ b/tests/neg/i2771.scala
@@ -14,7 +14,7 @@ object Test {
   type LL[F[_]] <: LB[F] // ok
 
   def foo[X[_] <: Any]() = ()
-  foo[Int]()  // an error would be raised later, during PostTyper.
+  foo[Int]()  // error: Int has wrong kind
 
   def bar[X, Y]() = ()
   bar[List, Int]()   // error: List has wrong kind
diff --git a/tests/neg/tcpoly_overloaded.scala b/tests/neg/tcpoly_overloaded.scala
index beefb652476e..6dd5fe3f0395 100644
--- a/tests/neg/tcpoly_overloaded.scala
+++ b/tests/neg/tcpoly_overloaded.scala
@@ -11,7 +11,7 @@ trait Monad[T <: Bound[T], MyType[x <: Bound[x]], Bound[_]] {
 
 trait Test {
   def moo: MList[Int]
-  class MList[T](el: T) extends Monad[T, List, Any] {  // error: does not conform to upper bound // error
+  class MList[T](el: T) extends Monad[T, List, Any] {  // error: wrong kind
     def flatMap[S <: RBound[S], RContainer[x <: RBound[x]], RBound[_],
             Result[x <: RBound[x]] <: Monad[x, RContainer, RBound]]
             (f: T => Result[S]): Result[S] = sys.error("foo")
@@ -21,5 +21,5 @@ trait Test {
     def flatMap[S]
             (f: T => List[S], foo: Int): List[S]  = sys.error("foo")
   }
-  val l: MList[String] = moo.flatMap[String, List, Any, MList]((x: Int) => new MList("String")) // error: does not conform to upper bound // error
+  val l: MList[String] = moo.flatMap[String, List, Any, MList]((x: Int) => new MList("String")) // error: wrong kind
 }