diff --git a/compiler/src/dotty/tools/dotc/core/TypeOps.scala b/compiler/src/dotty/tools/dotc/core/TypeOps.scala
index 739a06abb7f3..1caa3b7d3e3e 100644
--- a/compiler/src/dotty/tools/dotc/core/TypeOps.scala
+++ b/compiler/src/dotty/tools/dotc/core/TypeOps.scala
@@ -533,6 +533,18 @@ object TypeOps:
         val sym = tp.symbol
         forbidden.contains(sym)
 
+      /** We need to split the set into upper and lower approximations
+       *  only if it contains a local element. The idea here is that at the
+       *  time we perform an `avoid` all local elements are already accounted for
+       *  and no further elements will be added afterwards. So we can just keep
+       *  the set as it is. See comment by @linyxus on #16261.
+       */
+      override def needsRangeIfInvariant(refs: CaptureSet): Boolean =
+        refs.elems.exists {
+          case ref: TermRef => toAvoid(ref)
+          case _ => false
+        }
+
       override def apply(tp: Type): Type = tp match
         case tp: TypeVar if mapCtx.typerState.constraint.contains(tp) =>
           val lo = TypeComparer.instanceType(
diff --git a/compiler/src/dotty/tools/dotc/core/Types.scala b/compiler/src/dotty/tools/dotc/core/Types.scala
index 54bd0eafa064..61a8760e6c93 100644
--- a/compiler/src/dotty/tools/dotc/core/Types.scala
+++ b/compiler/src/dotty/tools/dotc/core/Types.scala
@@ -6027,8 +6027,11 @@ object Types {
             tp.derivedLambdaType(tp.paramNames, formals, restpe)
       }
 
+    /** Overridden in TypeOps.avoid */
+    protected def needsRangeIfInvariant(refs: CaptureSet): Boolean = true
+
     override def mapCapturingType(tp: Type, parent: Type, refs: CaptureSet, v: Int): Type =
-      if v == 0 then
+      if v == 0 && needsRangeIfInvariant(refs) then
         range(mapCapturingType(tp, parent, refs, -1), mapCapturingType(tp, parent, refs, 1))
       else
         super.mapCapturingType(tp, parent, refs, v)
diff --git a/tests/neg-custom-args/captures/try.check b/tests/neg-custom-args/captures/try.check
index 30ebb910d34d..13aff2661b85 100644
--- a/tests/neg-custom-args/captures/try.check
+++ b/tests/neg-custom-args/captures/try.check
@@ -1,8 +1,8 @@
 -- [E007] Type Mismatch Error: tests/neg-custom-args/captures/try.scala:23:49 ------------------------------------------
 23 |  val a = handle[Exception, CanThrow[Exception]] { // error
    |                                                 ^
-   |                                      Found:    ? ({*} CT[Exception]) -> {*} CT[? >: ? Exception <: ? Exception]
-   |                                      Required: CanThrow[Exception] => box {*} CT[Exception]
+   |                                                 Found:    ? ({*} CT[Exception]) -> CanThrow[? Exception]
+   |                                                 Required: CanThrow[Exception] => box {*} CT[Exception]
 24 |    (x: CanThrow[Exception]) => x
 25 |  }{
    |
diff --git a/tests/pos-custom-args/captures/i16226.scala b/tests/pos-custom-args/captures/i16226.scala
new file mode 100644
index 000000000000..8edf3f54d739
--- /dev/null
+++ b/tests/pos-custom-args/captures/i16226.scala
@@ -0,0 +1,14 @@
+@annotation.capability class Cap
+
+class LazyRef[T](val elem: () => T):
+  val get: {elem} () -> T = elem
+  def map[U](f: T => U): {f, this} LazyRef[U] =
+    new LazyRef(() => f(elem()))
+
+def map[A, B](ref: {*} LazyRef[A], f: A => B): {f, ref} LazyRef[B] =
+  new LazyRef(() => f(ref.elem()))
+
+def main(io: Cap) = {
+  def mapd[A, B]: ({io} LazyRef[A], A => B) => {*} LazyRef[B] =
+    (ref1, f1) => map[A, B](ref1, f1)
+}
diff --git a/tests/pos-custom-args/captures/i16226a.scala b/tests/pos-custom-args/captures/i16226a.scala
new file mode 100644
index 000000000000..444d7f2ed0d7
--- /dev/null
+++ b/tests/pos-custom-args/captures/i16226a.scala
@@ -0,0 +1,13 @@
+class Name
+class TermName extends Name
+class TypeName extends Name
+
+trait ParamInfo:
+  type ThisName <: Name
+  def variance: Long
+object ParamInfo:
+  type Of[N <: Name] = ParamInfo { type ThisName = N }
+
+def test(tparams1: List[ParamInfo{ type ThisName = TypeName }], tparams2: List[ParamInfo.Of[TypeName]]) =
+  tparams1.lazyZip(tparams2).map((p1, p2) => p1.variance + p2.variance)
+