diff --git a/pkg/sql/colexec/disk_spiller.go b/pkg/sql/colexec/disk_spiller.go
index 2e3ad36f3dd8..1b0dfdbd3885 100644
--- a/pkg/sql/colexec/disk_spiller.go
+++ b/pkg/sql/colexec/disk_spiller.go
@@ -239,8 +239,17 @@ func (d *diskSpillerBase) Close(ctx context.Context) error {
 		return nil
 	}
 	var retErr error
+	for _, input := range d.inputs {
+		if c, ok := input.(colexecop.Closer); ok {
+			if err := c.Close(ctx); err != nil {
+				retErr = err
+			}
+		}
+	}
 	if c, ok := d.inMemoryOp.(colexecop.Closer); ok {
-		retErr = c.Close(ctx)
+		if err := c.Close(ctx); err != nil {
+			retErr = err
+		}
 	}
 	if c, ok := d.diskBackedOp.(colexecop.Closer); ok {
 		if err := c.Close(ctx); err != nil {
diff --git a/pkg/sql/colexec/external_distinct_test.go b/pkg/sql/colexec/external_distinct_test.go
index 0b34d35da753..f35dd55d7d98 100644
--- a/pkg/sql/colexec/external_distinct_test.go
+++ b/pkg/sql/colexec/external_distinct_test.go
@@ -91,14 +91,8 @@ func TestExternalDistinct(t *testing.T) {
 				require.Equal(t, numExpectedClosers, len(closers))
 				return distinct, err
 			})
-			if tc.errorOnDup == "" || tc.noError {
-				// We don't check that all FDs were released if an error is
-				// expected to be returned because our utility closeIfCloser()
-				// doesn't handle multiple closers (which is always the case for
-				// the external distinct).
-				for i, sem := range semsToCheck {
-					require.Equal(t, 0, sem.GetCount(), "sem still reports open FDs at index %d", i)
-				}
+			for i, sem := range semsToCheck {
+				require.Equal(t, 0, sem.GetCount(), "sem still reports open FDs at index %d", i)
 			}
 		}
 	}
diff --git a/pkg/sql/colexec/parallel_unordered_synchronizer.go b/pkg/sql/colexec/parallel_unordered_synchronizer.go
index 3d561c2b7555..3151abe2362f 100644
--- a/pkg/sql/colexec/parallel_unordered_synchronizer.go
+++ b/pkg/sql/colexec/parallel_unordered_synchronizer.go
@@ -477,9 +477,10 @@ func (s *ParallelUnorderedSynchronizer) Close(ctx context.Context) error {
 	// Note that at this point we know that the input goroutines won't be
 	// spawned up (our consumer won't call Next/DrainMeta after calling Close),
 	// so it is safe to close all closers from this goroutine.
-	for _, span := range s.tracingSpans {
+	for i, span := range s.tracingSpans {
 		if span != nil {
 			span.Finish()
+			s.tracingSpans[i] = nil
 		}
 	}
 	var lastErr error
diff --git a/pkg/sql/colexec/serial_unordered_synchronizer.go b/pkg/sql/colexec/serial_unordered_synchronizer.go
index 02288277f4c6..1bd385848512 100644
--- a/pkg/sql/colexec/serial_unordered_synchronizer.go
+++ b/pkg/sql/colexec/serial_unordered_synchronizer.go
@@ -120,6 +120,7 @@ func (s *SerialUnorderedSynchronizer) Close(context.Context) error {
 	}
 	if s.span != nil {
 		s.span.Finish()
+		s.span = nil
 	}
 	return lastErr
 }
diff --git a/pkg/sql/colexecop/operator.go b/pkg/sql/colexecop/operator.go
index 86e75d750093..9ff092181c3d 100644
--- a/pkg/sql/colexecop/operator.go
+++ b/pkg/sql/colexecop/operator.go
@@ -143,7 +143,9 @@ type BufferingInMemoryOperator interface {
 type Closer interface {
 	// Close releases the resources associated with this Closer. If this Closer
 	// is an Operator, the implementation of Close must be safe to execute even
-	// if Operator.Init wasn't called.
+	// if Operator.Init wasn't called. Multiple calls to Close() are allowed,
+	// and most of the implementations should make all calls except for the
+	// first one no-ops.
 	//
 	// Unless the Closer derives its own context with a separate tracing span,
 	// the argument context rather than the one from Init() must be used