diff --git a/compiler/src/dotty/tools/dotc/core/Constraint.scala b/compiler/src/dotty/tools/dotc/core/Constraint.scala
index fb87aed77c41..b849c7aa7093 100644
--- a/compiler/src/dotty/tools/dotc/core/Constraint.scala
+++ b/compiler/src/dotty/tools/dotc/core/Constraint.scala
@@ -88,6 +88,8 @@ abstract class Constraint extends Showable {
    *   - Another type, indicating a solution for the parameter
    *
    * @pre  `this contains param`.
+   * @pre  `tp` does not contain top-level references to `param`
+   *       (see `validBoundsFor`)
    */
   def updateEntry(param: TypeParamRef, tp: Type)(using Context): This
 
@@ -172,6 +174,23 @@ abstract class Constraint extends Showable {
    */
   def occursAtToplevel(param: TypeParamRef, tp: Type)(using Context): Boolean
 
+  /** Sanitize `bound` to make it either a valid upper or lower bound for
+   *  `param` depending on `isUpper`.
+   *
+   *  Toplevel references to `param`, are replaced by `Any` if `isUpper` is true
+   *  and `Nothing` otherwise.
+   *
+   *  @see `occursAtTopLevel` for a definition of "toplevel"
+   *  @see `validBoundsFor` to sanitize both the lower and upper bound at once.
+   */
+  def validBoundFor(param: TypeParamRef, bound: Type, isUpper: Boolean)(using Context): Type
+
+  /** Sanitize `bounds` to make them valid constraints for `param`.
+   *
+   *  @see `validBoundFor` for details.
+   */
+  def validBoundsFor(param: TypeParamRef, bounds: TypeBounds)(using Context): Type
+
   /** A string that shows the reverse dependencies maintained by this constraint
    *  (coDeps and contraDeps for OrderingConstraints).
    */
diff --git a/compiler/src/dotty/tools/dotc/core/ConstraintHandling.scala b/compiler/src/dotty/tools/dotc/core/ConstraintHandling.scala
index c7c005b5220f..6207e0a3d728 100644
--- a/compiler/src/dotty/tools/dotc/core/ConstraintHandling.scala
+++ b/compiler/src/dotty/tools/dotc/core/ConstraintHandling.scala
@@ -257,7 +257,7 @@ trait ConstraintHandling {
   end LevelAvoidMap
 
   /** Approximate `rawBound` if needed to make it a legal bound of `param` by
-   *  avoiding wildcards and types with a level strictly greater than its
+   *  avoiding cycles, wildcards and types with a level strictly greater than its
    *  `nestingLevel`.
    *
    *  Note that level-checking must be performed here and cannot be delayed
@@ -283,7 +283,7 @@ trait ConstraintHandling {
         // This is necessary for i8900-unflip.scala to typecheck.
         val v = if necessaryConstraintsOnly then -this.variance else this.variance
         atVariance(v)(super.legalVar(tp))
-    approx(rawBound)
+    constraint.validBoundFor(param, approx(rawBound), isUpper)
   end legalBound
 
   protected def addOneBound(param: TypeParamRef, rawBound: Type, isUpper: Boolean)(using Context): Boolean =
@@ -413,8 +413,10 @@ trait ConstraintHandling {
 
     constraint = constraint.addLess(p2, p1, direction = if pKept eq p1 then KeepParam2 else KeepParam1)
 
-    val boundKept    = constraint.nonParamBounds(pKept).substParam(pRemoved, pKept)
-    var boundRemoved = constraint.nonParamBounds(pRemoved).substParam(pRemoved, pKept)
+    val boundKept    = constraint.validBoundsFor(pKept,
+      constraint.nonParamBounds(   pKept).substParam(pRemoved, pKept).bounds)
+    var boundRemoved = constraint.validBoundsFor(pKept,
+      constraint.nonParamBounds(pRemoved).substParam(pRemoved, pKept).bounds)
 
     if level1 != level2 then
       boundRemoved = LevelAvoidMap(-1, math.min(level1, level2))(boundRemoved)
diff --git a/compiler/src/dotty/tools/dotc/core/OrderingConstraint.scala b/compiler/src/dotty/tools/dotc/core/OrderingConstraint.scala
index 1f65fa324147..603d7a3cb0e3 100644
--- a/compiler/src/dotty/tools/dotc/core/OrderingConstraint.scala
+++ b/compiler/src/dotty/tools/dotc/core/OrderingConstraint.scala
@@ -525,20 +525,11 @@ class OrderingConstraint(private val boundsMap: ParamBounds,
 
 // ---------- Updates ------------------------------------------------------------
 
-  /** If `inst` is a TypeBounds, make sure it does not contain toplevel
-   *  references to `param` (see `Constraint#occursAtToplevel` for a definition
-   *  of "toplevel").
-   *  Any such references are replaced by `Nothing` in the lower bound and `Any`
-   *  in the upper bound.
-   *  References can be direct or indirect through instantiations of other
-   *  parameters in the constraint.
-   */
-  private def ensureNonCyclic(param: TypeParamRef, inst: Type)(using Context): Type =
-
-    def recur(tp: Type, fromBelow: Boolean): Type = tp match
+  def validBoundFor(param: TypeParamRef, bound: Type, isUpper: Boolean)(using Context): Type =
+    def recur(tp: Type): Type = tp match
       case tp: AndOrType =>
-        val r1 = recur(tp.tp1, fromBelow)
-        val r2 = recur(tp.tp2, fromBelow)
+        val r1 = recur(tp.tp1)
+        val r2 = recur(tp.tp2)
         if (r1 eq tp.tp1) && (r2 eq tp.tp2) then tp
         else tp.match
           case tp: OrType =>
@@ -547,35 +538,34 @@ class OrderingConstraint(private val boundsMap: ParamBounds,
             r1 & r2
       case tp: TypeParamRef =>
         if tp eq param then
-          if fromBelow then defn.NothingType else defn.AnyType
+          if isUpper then defn.AnyType else defn.NothingType
         else entry(tp) match
           case NoType => tp
-          case TypeBounds(lo, hi) => if lo eq hi then recur(lo, fromBelow) else tp
-          case inst => recur(inst, fromBelow)
+          case TypeBounds(lo, hi) => if lo eq hi then recur(lo) else tp
+          case inst => recur(inst)
       case tp: TypeVar =>
-        val underlying1 = recur(tp.underlying, fromBelow)
+        val underlying1 = recur(tp.underlying)
         if underlying1 ne tp.underlying then underlying1 else tp
       case CapturingType(parent, refs) =>
-        val parent1 = recur(parent, fromBelow)
+        val parent1 = recur(parent)
         if parent1 ne parent then tp.derivedCapturingType(parent1, refs) else tp
       case tp: AnnotatedType =>
-        val parent1 = recur(tp.parent, fromBelow)
+        val parent1 = recur(tp.parent)
         if parent1 ne tp.parent then tp.derivedAnnotatedType(parent1, tp.annot) else tp
       case _ =>
         val tp1 = tp.dealiasKeepAnnots
         if tp1 ne tp then
-          val tp2 = recur(tp1, fromBelow)
+          val tp2 = recur(tp1)
           if tp2 ne tp1 then tp2 else tp
         else tp
 
-    inst match
-      case bounds: TypeBounds =>
-        bounds.derivedTypeBounds(
-          recur(bounds.lo, fromBelow = true),
-          recur(bounds.hi, fromBelow = false))
-      case _ =>
-        inst
-  end ensureNonCyclic
+    recur(bound)
+  end validBoundFor
+
+  def validBoundsFor(param: TypeParamRef, bounds: TypeBounds)(using Context): Type =
+    bounds.derivedTypeBounds(
+      validBoundFor(param, bounds.lo, isUpper = false),
+      validBoundFor(param, bounds.hi, isUpper = true))
 
   /** Add the fact `param1 <: param2` to the constraint `current` and propagate
    *  `<:<` relationships between parameters ("edges") but not bounds.
@@ -658,9 +648,8 @@ class OrderingConstraint(private val boundsMap: ParamBounds,
     current1
   }
 
-  /** The public version of `updateEntry`. Guarantees that there are no cycles */
   def updateEntry(param: TypeParamRef, tp: Type)(using Context): This =
-    updateEntry(this, param, ensureNonCyclic(param, tp)).checkWellFormed()
+    updateEntry(this, param, tp).checkWellFormed()
 
   def addLess(param1: TypeParamRef, param2: TypeParamRef, direction: UnificationDirection)(using Context): This =
     order(this, param1, param2, direction).checkWellFormed()
@@ -703,7 +692,9 @@ class OrderingConstraint(private val boundsMap: ParamBounds,
 
       def replaceParamIn(other: TypeParamRef) =
         val oldEntry = current.entry(other)
-        val newEntry = current.ensureNonCyclic(other, oldEntry.substParam(param, replacement))
+        val newEntry = oldEntry.substParam(param, replacement) match
+          case tp: TypeBounds => validBoundsFor(other, tp)
+          case tp => tp
         current = boundsLens.update(this, current, other, newEntry)
         var oldDepEntry = oldEntry
         var newDepEntry = newEntry
diff --git a/compiler/test/dotty/tools/dotc/core/ConstraintsTest.scala b/compiler/test/dotty/tools/dotc/core/ConstraintsTest.scala
index 5ab162b9f05c..ad8578fa3e61 100644
--- a/compiler/test/dotty/tools/dotc/core/ConstraintsTest.scala
+++ b/compiler/test/dotty/tools/dotc/core/ConstraintsTest.scala
@@ -53,3 +53,27 @@ class ConstraintsTest:
         i"Merging constraints `?S <: ?T` and `Int <: ?S` should result in `Int <:< ?T`: ${ctx.typerState.constraint}")
     }
   end mergeBoundsTransitivity
+
+  @Test def validBoundsInit: Unit = inCompilerContext(
+    TestConfiguration.basicClasspath,
+    scalaSources = "trait A { def foo[S >: T <: T | Int, T <: String]: Any  }") {
+      val tvars = constrained(requiredClass("A").typeRef.select("foo".toTermName).info.asInstanceOf[TypeLambda], EmptyTree, alwaysAddTypeVars = true)._2
+      val List(s, t) = tvars.tpes
+
+      val TypeBounds(lo, hi) = ctx.typerState.constraint.entry(t.asInstanceOf[TypeVar].origin): @unchecked
+      assert(lo =:= defn.NothingType, i"Unexpected lower bound $lo for $t: ${ctx.typerState.constraint}")
+      assert(hi =:= defn.StringType, i"Unexpected upper bound $hi for $t: ${ctx.typerState.constraint}") // used to be Any
+  }
+
+  @Test def validBoundsUnify: Unit = inCompilerContext(
+    TestConfiguration.basicClasspath,
+    scalaSources = "trait A { def foo[S >: T <: T | Int, T <: String | Int]: Any  }") {
+      val tvars = constrained(requiredClass("A").typeRef.select("foo".toTermName).info.asInstanceOf[TypeLambda], EmptyTree, alwaysAddTypeVars = true)._2
+      val List(s, t) = tvars.tpes
+
+      s <:< t
+
+      val TypeBounds(lo, hi) = ctx.typerState.constraint.entry(t.asInstanceOf[TypeVar].origin): @unchecked
+      assert(lo =:= defn.NothingType, i"Unexpected lower bound $lo for $t: ${ctx.typerState.constraint}")
+      assert(hi =:= (defn.StringType | defn.IntType), i"Unexpected upper bound $hi for $t: ${ctx.typerState.constraint}")
+  }