diff --git a/runners/prism/java/build.gradle b/runners/prism/java/build.gradle
index a48973f65674..791952c625f4 100644
--- a/runners/prism/java/build.gradle
+++ b/runners/prism/java/build.gradle
@@ -98,6 +98,7 @@ def sickbayTests = [
     'org.apache.beam.sdk.transforms.ViewTest.testTriggeredLatestSingleton',
     // Requires Allowed Lateness, among others.
     'org.apache.beam.sdk.transforms.ParDoTest$TimerTests.testEventTimeTimerSetWithinAllowedLateness',
+    'org.apache.beam.sdk.transforms.ParDoTest$StateTests.testRequiresTimeSortedInputWithLateDataAndAllowedLateness',
     'org.apache.beam.sdk.testing.TestStreamTest.testFirstElementLate',
     'org.apache.beam.sdk.testing.TestStreamTest.testDiscardingMode',
     'org.apache.beam.sdk.testing.TestStreamTest.testEarlyPanesOfWindow',
@@ -160,6 +161,14 @@ def sickbayTests = [
     // TODO(https://github.com/apache/beam/issues/31231)
     'org.apache.beam.sdk.transforms.RedistributeTest.testRedistributePreservesMetadata',
 
+
+    // These tests fail once Late Data was being precisely dropped.
+    // They set a single element to be late data, and expect it (correctly) to be preserved.
+    // Since presently, these are treated as No-ops, the fix is to disable the
+    // dropping behavior when a stage's input is a Reshuffle/Redistribute transform.
+    'org.apache.beam.sdk.transforms.ReshuffleTest.testReshuffleWithTimestampsStreaming',
+    'org.apache.beam.sdk.transforms.RedistributeTest.testRedistributeWithTimestampsStreaming',
+
     // Prism isn't handling Java's side input views properly.
     // https://github.com/apache/beam/issues/32932
     // java.lang.IllegalArgumentException: PCollection with more than one element accessed as a singleton view.
@@ -177,13 +186,6 @@ def sickbayTests = [
     // java.lang.IllegalStateException: java.io.EOFException
     'org.apache.beam.sdk.transforms.ViewTest.testSideInputWithNestedIterables',
 
-    // Requires Time Sorted Input
-    'org.apache.beam.sdk.transforms.ParDoTest$StateTests.testRequiresTimeSortedInput',
-    'org.apache.beam.sdk.transforms.ParDoTest$StateTests.testRequiresTimeSortedInputWithTestStream',
-    'org.apache.beam.sdk.transforms.ParDoTest$StateTests.testRequiresTimeSortedInputWithLateDataAndAllowedLateness',
-    'org.apache.beam.sdk.transforms.ParDoTest$StateTests.testTwoRequiresTimeSortedInputWithLateData',
-    'org.apache.beam.sdk.transforms.ParDoTest$StateTests.testRequiresTimeSortedInputWithLateData',
-
     // Missing output due to processing time timer skew.
     'org.apache.beam.sdk.transforms.ParDoTest$TimestampTests.testProcessElementSkew',
 
diff --git a/sdks/go/pkg/beam/runners/prism/internal/engine/elementmanager.go b/sdks/go/pkg/beam/runners/prism/internal/engine/elementmanager.go
index 3cfcf9ef8c0e..bb3c8ceceeb8 100644
--- a/sdks/go/pkg/beam/runners/prism/internal/engine/elementmanager.go
+++ b/sdks/go/pkg/beam/runners/prism/internal/engine/elementmanager.go
@@ -1179,6 +1179,18 @@ func makeStageState(ID string, inputIDs, outputIDs []string, sides []LinkID) *st
 func (ss *stageState) AddPending(newPending []element) int {
 	ss.mu.Lock()
 	defer ss.mu.Unlock()
+	// TODO(#https://github.com/apache/beam/issues/31438):
+	// Adjust with AllowedLateness
+	// Data that arrives after the *output* watermark is late.
+	threshold := ss.output
+	origPending := make([]element, 0, ss.pending.Len())
+	for _, e := range newPending {
+		if e.window.MaxTimestamp() < threshold {
+			continue
+		}
+		origPending = append(origPending, e)
+	}
+	newPending = origPending
 	if ss.stateful {
 		if ss.pendingByKeys == nil {
 			ss.pendingByKeys = map[string]*dataAndTimers{}
diff --git a/sdks/go/pkg/beam/runners/prism/internal/handlepardo.go b/sdks/go/pkg/beam/runners/prism/internal/handlepardo.go
index 13e9b6f1b79d..7ac472251f61 100644
--- a/sdks/go/pkg/beam/runners/prism/internal/handlepardo.go
+++ b/sdks/go/pkg/beam/runners/prism/internal/handlepardo.go
@@ -84,9 +84,12 @@ func (h *pardo) PrepareTransform(tid string, t *pipepb.PTransform, comps *pipepb
 
 		// At their simplest, we don't need to do anything special at pre-processing time, and simply pass through as normal.
 
-		// StatefulDoFns need to be marked as being roots.
+		// ForceRoots cause fusion breaks in the optimized graph.
+		// StatefulDoFns need to be marked as being roots, for correct per-key state handling.
+		// Prism already sorts input elements for a stage by EventTime, so a fusion break enables the sorted behavior.
 		var forcedRoots []string
-		if len(pdo.StateSpecs)+len(pdo.TimerFamilySpecs) > 0 {
+		if len(pdo.GetStateSpecs())+len(pdo.GetTimerFamilySpecs()) > 0 ||
+			pdo.GetRequiresTimeSortedInput() {
 			forcedRoots = append(forcedRoots, tid)
 		}
 
diff --git a/sdks/go/pkg/beam/runners/prism/internal/jobservices/job.go b/sdks/go/pkg/beam/runners/prism/internal/jobservices/job.go
index 4be64e5a9c80..f186b11fd1d8 100644
--- a/sdks/go/pkg/beam/runners/prism/internal/jobservices/job.go
+++ b/sdks/go/pkg/beam/runners/prism/internal/jobservices/job.go
@@ -47,6 +47,7 @@ var supportedRequirements = map[string]struct{}{
 	urns.RequirementStatefulProcessing: {},
 	urns.RequirementBundleFinalization: {},
 	urns.RequirementOnWindowExpiration: {},
+	urns.RequirementTimeSortedInput:    {},
 }
 
 // TODO, move back to main package, and key off of executor handlers?
diff --git a/sdks/java/core/src/test/java/org/apache/beam/sdk/transforms/ParDoTest.java b/sdks/java/core/src/test/java/org/apache/beam/sdk/transforms/ParDoTest.java
index 742547b9b6c3..8409133772eb 100644
--- a/sdks/java/core/src/test/java/org/apache/beam/sdk/transforms/ParDoTest.java
+++ b/sdks/java/core/src/test/java/org/apache/beam/sdk/transforms/ParDoTest.java
@@ -3764,7 +3764,9 @@ public void testRequiresTimeSortedInputWithLateData() {
         if (stamp == 100) {
           // advance watermark when we have 100 remaining elements
           // all the rest are going to be late elements
-          input = input.advanceWatermarkTo(Instant.ofEpochMilli(stamp));
+          input =
+              input.advanceWatermarkTo(
+                  GlobalWindow.INSTANCE.maxTimestamp().plus(Duration.standardSeconds(1)));
         }
       }
       testTimeSortedInput(
@@ -3796,7 +3798,9 @@ public void testTwoRequiresTimeSortedInputWithLateData() {
         if (stamp == 100) {
           // advance watermark when we have 100 remaining elements
           // all the rest are going to be late elements
-          input = input.advanceWatermarkTo(Instant.ofEpochMilli(stamp));
+          input =
+              input.advanceWatermarkTo(
+                  GlobalWindow.INSTANCE.maxTimestamp().plus(Duration.standardSeconds(1)));
         }
       }
       // apply the sorted function for the first time