diff --git a/MonteCarloMarginalizeCode/Code/bin/util_RandomizeOverlapOrder.py b/MonteCarloMarginalizeCode/Code/bin/util_RandomizeOverlapOrder.py
index 6869ca4e5..632d5c2c7 100755
--- a/MonteCarloMarginalizeCode/Code/bin/util_RandomizeOverlapOrder.py
+++ b/MonteCarloMarginalizeCode/Code/bin/util_RandomizeOverlapOrder.py
@@ -28,6 +28,7 @@
 optp.add_option("--fref",default=20,type=float,help="Reference frequency. Depending on approximant and age of implementation, may be ignored")
 optp.add_option("--n-min",default=20,type=int,help="Minimum size of file to include. NOT USED")
 optp.add_option("--output-file",default='merged_output',type=str,help="Merged output file")
+optp.add_option("--preserve-block-order",action='store_true',help="Do NOT interleave across input files; append each file's block in file order. This is the pre-2026-08 behaviour and is only for reproducing runs made before the interleave fix.")
 optp.add_option("--verbose",action='store_true',help="Print messages")
 opts, args = optp.parse_args()
 
@@ -61,4 +62,14 @@
     P_to_add = [P_list_list[indx][a] for a in indx_to_take]
     P_list += P_to_add
 
+# Interleave ACROSS files.  The draw above randomises only WITHIN each file, and the blocks are
+# appended in file order, so the merged output is [file0][file1]...[fileN].  That is invisible to a
+# consumer that reads the whole file, but the nested ILE reads only a PREFIX (measured: the first
+# 3000 rows), so it saw just the first few workers -- with 25 workers x 800, four of them, and with
+# 6 x 3334, only the first.  That is precisely the "accidentally using only the output from one of
+# them" failure this tool exists to prevent.  The hyperpipeline branch of write_joingrids_sub
+# already does this ("shuffle so spokes are interleaved"); this brings the XML path into line.
+if not opts.preserve_block_order:
+    P_list = [P_list[k] for k in np.random.permutation(len(P_list))]
+
 lalsimutils.ChooseWaveformParams_array_to_xml(P_list,opts.output_file)