diff --git a/R/BatchtoolsParam-class.R b/R/BatchtoolsParam-class.R
index 316cd98..5a348b6 100644
--- a/R/BatchtoolsParam-class.R
+++ b/R/BatchtoolsParam-class.R
@@ -461,8 +461,6 @@ setMethod("bpiterate", c("ANY", "ANY", "BatchtoolsParam"),
     FUN <- match.fun(FUN)
 
     if (missing(REDUCE)) {
-        if (reduce.in.order)
-            stop("REDUCE must be provided when 'reduce.in.order = TRUE'")
         if (!missing(init))
             stop("REDUCE must be provided when 'init' is given")
     }
diff --git a/inst/unitTests/test_BatchtoolsParam.R b/inst/unitTests/test_BatchtoolsParam.R
index c44af20..f22ac37 100644
--- a/inst/unitTests/test_BatchtoolsParam.R
+++ b/inst/unitTests/test_BatchtoolsParam.R
@@ -423,12 +423,25 @@ test_BatchtoolsParam_bpiterate <- function() {
     target <- list(105, 205, 305, 405, 505)
     checkIdentical(target, res)
 
+    ## Test ordered results without REDUCE on multicore
+    param <- BatchtoolsParam()
+    res <- bpiterate(ITER=ITER(), FUN=FUN, k=5,
+                     reduce.in.order=TRUE,
+                     BPPARAM=param)
+    checkIdentical(target, res)
+
     ## socket cluster
     param <- BatchtoolsParam(cluster="socket")
     res <- bpiterate(ITER=ITER(), FUN=FUN, k=5, BPPARAM=param)
     ## Check Identical result
     checkIdentical(target, res)
 
+    ## Test ordered results without REDUCE on socket
+    res <- bpiterate(ITER=ITER(), FUN=FUN, k=5,
+                     reduce.in.order=TRUE,
+                     BPPARAM=param)
+    checkIdentical(target, res)
+
     ## Test REDUCE on socket
     res <- bpiterate(ITER=ITER(), FUN=FUN, k=5,
                      REDUCE=`+`,