diff --git a/NEWS.md b/NEWS.md
index fa384dc10..f5fbd2248 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -123,6 +123,8 @@ rowwiseDT(
 
 16. Joins of `integer64` and `double` columns succeed when the `double` column has lossless `integer64` representation, [#4167](https://github.com/Rdatatable/data.table/issues/4167) and [#6625](https://github.com/Rdatatable/data.table/issues/6625). Previously, this only worked when the double column had lossless _32-bit_ integer representation. Thanks @MichaelChirico for the reports and fix.
 
+17. `DT[order(...)]` better matches `base::order()` behavior by (1) recognizing the `method=` argument (and erroring since this is not supported) and (2) accepting a vector of `TRUE`/`FALSE` in `decreasing=` as an alternative to using `-a` to convey "sort `a` decreasing", [#4456](https://github.com/Rdatatable/data.table/issues/4456). Thanks @jangorecki for the FR and @MichaelChirico for the PR.
+
 ## NOTES
 
 1. There is a new vignette on joins! See `vignette("datatable-joins")`. Thanks to Angel Feliz for authoring it! Feedback welcome. This vignette has been highly requested since 2017: [#2181](https://github.com/Rdatatable/data.table/issues/2181).
diff --git a/R/setkey.R b/R/setkey.R
index 11b02ec2d..58c5af5ea 100644
--- a/R/setkey.R
+++ b/R/setkey.R
@@ -160,8 +160,10 @@ forderv = function(x, by=seq_along(x), retGrp=FALSE, retStats=retGrp, sort=TRUE,
   .Call(CforderReuseSorting, x, by, retGrp, retStats, sort, order, na.last, reuseSorting)  # returns integer() if already sorted, regardless of sort=TRUE|FALSE
 }
 
-forder = function(..., na.last=TRUE, decreasing=FALSE)
+forder = function(..., na.last=TRUE, decreasing=FALSE, method="radix")
 {
+  if (method != "radix") stopf("data.table has no support for sorting by method='%s'. Use base::order(), not order(), if you really need this.", method)
+  stopifnot(is.logical(decreasing), length(decreasing) > 0L, !is.na(decreasing))
   sub = substitute(list(...))
   tt = vapply_1b(sub, function(x) is.null(x) || (is.symbol(x) && !nzchar(x)))
   if (any(tt)) sub[tt] = NULL  # remove any NULL or empty arguments; e.g. test 1962.052: forder(DT, NULL) and forder(DT, )
@@ -169,8 +171,8 @@ forder = function(..., na.last=TRUE, decreasing=FALSE)
   asc = rep.int(1L, length(sub)-1L)  # ascending (1) or descending (-1) per column
   # the idea here is to intercept - (and unusual --+ deriving from built expressions) before vectors in forder(DT, -colA, colB) so that :
   # 1) - on character vector works; ordinarily in R that fails with type error
-  # 2) each column/expression can have its own +/- more easily that having to use a separate decreasing=TRUE/FALSE
-  # 3) we can pass the decreasing (-) flag to C and avoid what normally happens in R; i.e. allocate a new vector and apply - to every element first
+  # 2) each column/expression can have its own +/- more easily than having to use a separate decreasing=TRUE/FALSE
+  # 3) we can pass the decreasing (-) flag to C and avoid what normally happens in R; i.e. allocate a new vector and negate every element first
   # We intercept the unevaluated expressions and massage them before evaluating in with(DT) scope or not depending on the first item.
   for (i in seq.int(2L, length(sub))) {
     v = sub[[i]]
@@ -193,8 +195,16 @@ forder = function(..., na.last=TRUE, decreasing=FALSE)
   } else {
     data = eval(sub, parent.frame(), parent.frame())
   }
-  stopifnot(isTRUEorFALSE(decreasing))
-  o = forderv(data, seq_along(data), retGrp=FALSE, retStats=FALSE, sort=TRUE, order=if (decreasing) -asc else asc, na.last=na.last)
+  if (length(decreasing) > 1L) {
+    if (any(asc < 0L)) stopf("Mixing '-' with vector decreasing= is not supported.")
+    if (length(decreasing) != length(asc)) stopf("decreasing= has length %d applied to sorting %d columns.", length(decreasing), length(asc))
+    orderArg = fifelse(decreasing, -asc, asc)
+  } else if (decreasing) {
+    orderArg = -asc
+  } else {
+    orderArg = asc
+  }
+  o = forderv(data, seq_along(data), retGrp=FALSE, retStats=FALSE, sort=TRUE, order=orderArg, na.last=na.last)
   if (!length(o) && length(data)>=1L) o = seq_along(data[[1L]]) else o
   o
 }
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 657478c61..b930aca76 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -13614,8 +13614,9 @@ test(1962.0482, forder(L), 3:1)
 test(1962.0483, forder(), NULL)
 setDT(DT)
 test(1962.049, forder(DT[ , 0L]), error = 'Attempting to order a 0-column')
-test(1962.050, forder(DT, decreasing = NA), error = base_messages$stopifnot('isTRUEorFALSE(decreasing)'))
-test(1962.051, forder(DT, decreasing = 1.4), error = base_messages$stopifnot('isTRUEorFALSE(decreasing)'))
+test(1962.050, forder(DT, decreasing = NA), error = base_messages$stopifnot('!is.na(decreasing)'))
+test(1962.0510, forder(DT, decreasing = 1.4), error = base_messages$stopifnot('is.logical(decreasing)'))
+test(1962.0511, forder(DT, decreasing=logical()), error=base_messages$stopifnot('length(decreasing) > 0L'))
 test(1962.052, forder(DT, NULL), 3:1)
 test(1962.053, forder(DT), 3:1)
 test(1962.054, forder(DT, ), 3:1)
@@ -20697,3 +20698,9 @@ if (test_bit64) {
   test(2300.3, DT1[DT2, on='id'], error="Incompatible join types")
   test(2300.4, DT2[DT1, on='id'], error="Incompatible join types")
 }
+
+# interpret more arguments to order() correctly when translating to forder(), #4456
+DT = data.table(a=rep(1:3, 4), b=rep(1:2, 6))
+test(2301.1, DT[order(a, method="auto")], error="no support for sorting by method='auto'")
+test(2301.2, DT[order(a, b, decreasing=c(TRUE, FALSE))], DT[order(-a, b)])
+test(2301.3, DT[order(a, -b, decreasing=c(TRUE, TRUE))], error="Mixing '-' with vector decreasing")