diff --git a/crates/bevy_ecs/src/lib.rs b/crates/bevy_ecs/src/lib.rs
index ad93f91d0d150..e2f62cca07a7c 100644
--- a/crates/bevy_ecs/src/lib.rs
+++ b/crates/bevy_ecs/src/lib.rs
@@ -29,8 +29,8 @@ pub mod prelude {
         query::{Added, AnyOf, ChangeTrackers, Changed, Or, QueryState, With, Without},
         schedule::{
             AmbiguitySetLabel, ExclusiveSystemDescriptorCoercion, ParallelSystemDescriptorCoercion,
-            RunCriteria, RunCriteriaDescriptorCoercion, RunCriteriaLabel, RunCriteriaPiping,
-            Schedule, Stage, StageLabel, State, SystemLabel, SystemSet, SystemStage,
+            RunCriteria, RunCriteriaDescriptorCoercion, RunCriteriaLabel, Schedule, Stage,
+            StageLabel, State, SystemLabel, SystemSet, SystemStage,
         },
         system::{
             Commands, In, IntoChainSystem, IntoExclusiveSystem, IntoSystem, Local, NonSend,
diff --git a/crates/bevy_ecs/src/schedule/run_criteria.rs b/crates/bevy_ecs/src/schedule/run_criteria.rs
index f5aa1e0e60b92..7c7b9ecee4f55 100644
--- a/crates/bevy_ecs/src/schedule/run_criteria.rs
+++ b/crates/bevy_ecs/src/schedule/run_criteria.rs
@@ -240,12 +240,6 @@ where
     }
 }
 
-impl IntoRunCriteria<BoxedRunCriteriaLabel> for BoxedRunCriteriaLabel {
-    fn into(self) -> RunCriteriaDescriptorOrLabel {
-        RunCriteriaDescriptorOrLabel::Label(self)
-    }
-}
-
 impl<L> IntoRunCriteria<BoxedRunCriteriaLabel> for L
 where
     L: RunCriteriaLabel,
@@ -357,44 +351,16 @@ pub struct RunCriteria {
 impl RunCriteria {
     /// Constructs a new run criteria that will retrieve the result of the criteria `label`
     /// and pipe it as input to `system`.
-    pub fn pipe(
+    pub fn pipe<P>(
         label: impl RunCriteriaLabel,
-        system: impl System<In = ShouldRun, Out = ShouldRun>,
+        system: impl IntoSystem<ShouldRun, ShouldRun, P>,
     ) -> RunCriteriaDescriptor {
-        label.pipe(system)
-    }
-}
-
-pub trait RunCriteriaPiping {
-    /// See [`RunCriteria::pipe()`].
-    // TODO: Support `IntoSystem` here instead, and stop using
-    // `IntoSystem::into_system` in the call sites
-    fn pipe(self, system: impl System<In = ShouldRun, Out = ShouldRun>) -> RunCriteriaDescriptor;
-}
-
-impl RunCriteriaPiping for BoxedRunCriteriaLabel {
-    fn pipe(self, system: impl System<In = ShouldRun, Out = ShouldRun>) -> RunCriteriaDescriptor {
-        RunCriteriaDescriptor {
-            system: RunCriteriaSystem::Piped(Box::new(system)),
-            label: None,
-            duplicate_label_strategy: DuplicateLabelStrategy::Panic,
-            before: vec![],
-            after: vec![self],
-        }
-    }
-}
-
-impl<L> RunCriteriaPiping for L
-where
-    L: RunCriteriaLabel,
-{
-    fn pipe(self, system: impl System<In = ShouldRun, Out = ShouldRun>) -> RunCriteriaDescriptor {
         RunCriteriaDescriptor {
-            system: RunCriteriaSystem::Piped(Box::new(system)),
+            system: RunCriteriaSystem::Piped(Box::new(IntoSystem::into_system(system))),
             label: None,
             duplicate_label_strategy: DuplicateLabelStrategy::Panic,
             before: vec![],
-            after: vec![Box::new(self)],
+            after: vec![Box::new(label)],
         }
     }
 }
diff --git a/crates/bevy_ecs/src/schedule/stage.rs b/crates/bevy_ecs/src/schedule/stage.rs
index dd8d9976da48f..f53ad9dc49d39 100644
--- a/crates/bevy_ecs/src/schedule/stage.rs
+++ b/crates/bevy_ecs/src/schedule/stage.rs
@@ -946,10 +946,10 @@ mod tests {
         query::{ChangeTrackers, Changed},
         schedule::{
             BoxedSystemLabel, ExclusiveSystemDescriptorCoercion, ParallelSystemDescriptorCoercion,
-            RunCriteria, RunCriteriaDescriptorCoercion, RunCriteriaPiping, ShouldRun,
-            SingleThreadedExecutor, Stage, SystemSet, SystemStage,
+            RunCriteria, RunCriteriaDescriptorCoercion, ShouldRun, SingleThreadedExecutor, Stage,
+            SystemSet, SystemStage,
         },
-        system::{In, IntoExclusiveSystem, IntoSystem, Local, Query, ResMut},
+        system::{In, IntoExclusiveSystem, Local, Query, ResMut},
         world::World,
     };
 
@@ -1475,25 +1475,25 @@ mod tests {
                 ShouldRun::No
             }
         }
-        let mut stage = SystemStage::parallel()
-            .with_system(make_parallel(0).label("0"))
-            .with_system(
-                make_parallel(1)
-                    .label("1")
-                    .after("0")
-                    .with_run_criteria(every_other_time.label("every other time")),
-            )
-            .with_system(make_parallel(2).label("2").after("1").with_run_criteria(
-                RunCriteria::pipe("every other time", IntoSystem::into_system(eot_piped)),
-            ))
-            .with_system(
-                make_parallel(3).label("3").after("2").with_run_criteria(
-                    "every other time"
-                        .pipe(IntoSystem::into_system(eot_piped))
-                        .label("piped"),
-                ),
-            )
-            .with_system(make_parallel(4).after("3").with_run_criteria("piped"));
+        let mut stage =
+            SystemStage::parallel()
+                .with_system(make_parallel(0).label("0"))
+                .with_system(
+                    make_parallel(1)
+                        .label("1")
+                        .after("0")
+                        .with_run_criteria(every_other_time.label("every other time")),
+                )
+                .with_system(
+                    make_parallel(2)
+                        .label("2")
+                        .after("1")
+                        .with_run_criteria(RunCriteria::pipe("every other time", eot_piped)),
+                )
+                .with_system(make_parallel(3).label("3").after("2").with_run_criteria(
+                    RunCriteria::pipe("every other time", eot_piped).label("piped"),
+                ))
+                .with_system(make_parallel(4).after("3").with_run_criteria("piped"));
         for _ in 0..4 {
             stage.run(&mut world);
         }
diff --git a/examples/ecs/system_sets.rs b/examples/ecs/system_sets.rs
index fffba8b1b1910..642f9f49d2810 100644
--- a/examples/ecs/system_sets.rs
+++ b/examples/ecs/system_sets.rs
@@ -70,10 +70,7 @@ fn main() {
                 // Here we create a _not done_ criteria by piping the output of
                 // the `is_done` system and inverting the output.
                 // Notice a string literal also works as a label.
-                .with_run_criteria(RunCriteria::pipe(
-                    "is_done_label",
-                    IntoSystem::into_system(inverse),
-                ))
+                .with_run_criteria(RunCriteria::pipe("is_done_label", inverse))
                 // `collision` and `sfx` are not ordered with respect to
                 // each other, and may run in any order
                 .with_system(collision)