diff --git a/compiler/src/dotty/tools/dotc/ast/Desugar.scala b/compiler/src/dotty/tools/dotc/ast/Desugar.scala
index a7586f876435..31ba7ae10b95 100644
--- a/compiler/src/dotty/tools/dotc/ast/Desugar.scala
+++ b/compiler/src/dotty/tools/dotc/ast/Desugar.scala
@@ -1114,9 +1114,7 @@ object desugar {
         Apply(Select(Apply(Ident(nme.StringContext), strs), id), elems)
       case InfixOp(l, op, r) =>
         if (ctx.mode is Mode.Type)
-          if (!op.isBackquoted && op.name == tpnme.raw.AMP) AndTypeTree(l, r)     // l & r
-          else if (!op.isBackquoted && op.name == tpnme.raw.BAR) OrTypeTree(l, r) // l | r
-          else AppliedTypeTree(op, l :: r :: Nil) // op[l, r]
+          AppliedTypeTree(op, l :: r :: Nil) // op[l, r]
         else {
           assert(ctx.mode is Mode.Pattern) // expressions are handled separately by `binop`
           Apply(op, l :: r :: Nil) // op(l, r)
diff --git a/compiler/src/dotty/tools/dotc/parsing/Parsers.scala b/compiler/src/dotty/tools/dotc/parsing/Parsers.scala
index edaf6850d8cf..92a2a650d028 100644
--- a/compiler/src/dotty/tools/dotc/parsing/Parsers.scala
+++ b/compiler/src/dotty/tools/dotc/parsing/Parsers.scala
@@ -41,6 +41,25 @@ object Parsers {
     def nonePositive: Boolean = parCounts forall (_ <= 0)
   }
 
+  /** Checks whether `t` is a wildcard type.
+   *  If it is, returns the [[Position]] where the wildcard occurs.
+   */
+  @tailrec
+  final def findWildcardType(t: Tree): Option[Position] = t match {
+    case TypeBoundsTree(_, _) => Some(t.pos)
+    case Parens(t1) => findWildcardType(t1)
+    case Annotated(t1, _) => findWildcardType(t1)
+    case _ => None
+  }
+
+  def rejectWildcard(t: Tree, report: Position => Unit, fallbackTree: Tree): Tree =
+    findWildcardType(t) match {
+      case Some(wildcardPos) =>
+        report(wildcardPos)
+        fallbackTree
+      case None => t
+    }
+
   @sharable object Location extends Enumeration {
     val InParens, InBlock, InPattern, ElseWhere = Value
   }
@@ -452,7 +471,7 @@ object Parsers {
       if (isLeftAssoc(op1) != op2LeftAssoc)
         syntaxError(MixedLeftAndRightAssociativeOps(op1, op2, op2LeftAssoc), offset)
 
-    def reduceStack(base: List[OpInfo], top: Tree, prec: Int, leftAssoc: Boolean, op2: Name): Tree = {
+    def reduceStack(base: List[OpInfo], top: Tree, prec: Int, leftAssoc: Boolean, op2: Name, isType: Boolean): Tree = {
       if (opStack != base && precedence(opStack.head.operator.name) == prec)
         checkAssoc(opStack.head.offset, opStack.head.operator.name, op2, leftAssoc)
       def recur(top: Tree): Tree = {
@@ -464,7 +483,15 @@ object Parsers {
             opStack = opStack.tail
             recur {
               atPos(opInfo.operator.pos union opInfo.operand.pos union top.pos) {
-                InfixOp(opInfo.operand, opInfo.operator, top)
+                val op = opInfo.operator
+                val l = opInfo.operand
+                val r = top
+                if (isType && !op.isBackquoted && op.name == tpnme.raw.BAR) {
+                  OrTypeTree(checkWildcard(l), checkWildcard(r))
+                } else if (isType && !op.isBackquoted && op.name == tpnme.raw.AMP) {
+                  AndTypeTree(checkWildcard(l), checkWildcard(r))
+                } else
+                  InfixOp(l, op, r)
               }
             }
           }
@@ -488,20 +515,20 @@ object Parsers {
       var top = first
       while (isIdent && isOperator) {
         val op = if (isType) typeIdent() else termIdent()
-        top = reduceStack(base, top, precedence(op.name), isLeftAssoc(op.name), op.name)
+        top = reduceStack(base, top, precedence(op.name), isLeftAssoc(op.name), op.name, isType)
         opStack = OpInfo(top, op, in.offset) :: opStack
         newLineOptWhenFollowing(canStartOperand)
         if (maybePostfix && !canStartOperand(in.token)) {
           val topInfo = opStack.head
           opStack = opStack.tail
-          val od = reduceStack(base, topInfo.operand, 0, true, in.name)
+          val od = reduceStack(base, topInfo.operand, 0, true, in.name, isType)
           return atPos(startOffset(od), topInfo.offset) {
             PostfixOp(od, topInfo.operator)
           }
         }
         top = operand()
       }
-      reduceStack(base, top, 0, true, in.name)
+      reduceStack(base, top, 0, true, in.name, isType)
     }
 
 /* -------- IDENTIFIERS AND LITERALS ------------------------------------------- */
@@ -709,15 +736,7 @@ object Parsers {
     /** Same as [[typ]], but if this results in a wildcard it emits a syntax error and
      *  returns a tree for type `Any` instead.
      */
-    def toplevelTyp(): Tree = {
-      val t = typ()
-      findWildcardType(t) match {
-        case Some(wildcardPos) =>
-          syntaxError(UnboundWildcardType(), wildcardPos)
-          scalaAny
-        case None => t
-      }
-    }
+    def toplevelTyp(): Tree = checkWildcard(typ())
 
     /** Type        ::=  [FunArgMods] FunArgTypes `=>' Type
      *                |  HkTypeParamClause `->' Type
@@ -784,7 +803,7 @@ object Parsers {
           val start = in.offset
           val tparams = typeParamClause(ParamOwner.TypeParam)
           if (in.token == ARROW)
-            atPos(start, in.skipToken())(LambdaTypeTree(tparams, typ()))
+            atPos(start, in.skipToken())(LambdaTypeTree(tparams, toplevelTyp()))
           else { accept(ARROW); typ() }
         }
         else infixType()
@@ -822,7 +841,7 @@ object Parsers {
 
     def refinedTypeRest(t: Tree): Tree = {
       newLineOptWhenFollowedBy(LBRACE)
-      if (in.token == LBRACE) refinedTypeRest(atPos(startOffset(t)) { RefinedTypeTree(t, refinement()) })
+      if (in.token == LBRACE) refinedTypeRest(atPos(startOffset(t)) { RefinedTypeTree(checkWildcard(t), refinement()) })
       else t
     }
 
@@ -886,7 +905,7 @@ object Parsers {
     private def simpleTypeRest(t: Tree): Tree = in.token match {
       case HASH => simpleTypeRest(typeProjection(t))
       case LBRACKET => simpleTypeRest(atPos(startOffset(t)) {
-        AppliedTypeTree(t, typeArgs(namedOK = false, wildOK = true)) })
+        AppliedTypeTree(checkWildcard(t), typeArgs(namedOK = false, wildOK = true)) })
       case _ => t
     }
 
@@ -917,7 +936,7 @@ object Parsers {
           else Nil
         first :: rest
       }
-      def typParser() = if (wildOK) typ() else toplevelTyp()
+      def typParser() = checkWildcard(typ(), wildOK)
       if (namedOK && in.token == IDENTIFIER)
         typParser() match {
           case Ident(name) if in.token == EQUALS =>
@@ -1001,16 +1020,8 @@ object Parsers {
       else if (location == Location.InPattern) refinedType()
       else infixType()
 
-    /** Checks whether `t` is a wildcard type.
-     *  If it is, returns the [[Position]] where the wildcard occurs.
-     */
-    @tailrec
-    private final def findWildcardType(t: Tree): Option[Position] = t match {
-      case TypeBoundsTree(_, _) => Some(t.pos)
-      case Parens(t1) => findWildcardType(t1)
-      case Annotated(t1, _) => findWildcardType(t1)
-      case _ => None
-    }
+    def checkWildcard(t: Tree, wildOK: Boolean = false, fallbackTree: Tree = scalaAny): Tree =
+      if (wildOK) t else rejectWildcard(t, syntaxError(UnboundWildcardType(), _), fallbackTree)
 
 /* ----------- EXPRESSIONS ------------------------------------------------ */
 
@@ -2148,7 +2159,7 @@ object Parsers {
         in.token match {
           case EQUALS =>
             in.nextToken()
-            TypeDef(name, lambdaAbstract(tparams, typ())).withMods(mods).setComment(in.getDocComment(start))
+            TypeDef(name, lambdaAbstract(tparams, toplevelTyp())).withMods(mods).setComment(in.getDocComment(start))
           case SUPERTYPE | SUBTYPE | SEMI | NEWLINE | NEWLINES | COMMA | RBRACE | EOF =>
             TypeDef(name, lambdaAbstract(tparams, typeBounds())).withMods(mods).setComment(in.getDocComment(start))
           case _ =>
@@ -2276,7 +2287,8 @@ object Parsers {
     /** ConstrApp         ::=  SimpleType {ParArgumentExprs}
      */
     val constrApp = () => {
-      val t = annotType()
+      // Using Ident(nme.ERROR) to avoid causing cascade errors on non-user-written code
+      val t = checkWildcard(annotType(), fallbackTree = Ident(nme.ERROR))
       if (in.token == LPAREN) parArgumentExprss(wrapNew(t))
       else t
     }
diff --git a/tests/neg/i4373.scala b/tests/neg/i4373.scala
new file mode 100644
index 000000000000..349985521856
--- /dev/null
+++ b/tests/neg/i4373.scala
@@ -0,0 +1,23 @@
+trait Base
+trait TypeConstr[X]
+
+class X1[A >: _ | X1[_]] // error
+class X2[A >: _ & X2[_]] // error
+class X3[A >: X3[_] | _] // error
+class X4[A >: X4[_] & _] // error
+
+class A1 extends _ // error
+class A2 extends _ with _ // error // error
+class A3 extends Base with _ // error
+class A4 extends _ with Base // error
+
+object Test {
+  type T1 = _ // error
+  type T2 = _[Int] // error
+  type T3 = _ { type S } // error
+  type T4 = [X] => _ // error
+
+  // Open questions:
+  type T5 = TypeConstr[_ { type S }] // error
+  type T5 = TypeConstr[_[Int]] // error
+}