diff --git a/NEWS.md b/NEWS.md
index 58e9d6fbee..141385b010 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -282,6 +282,8 @@
 
 37. `rbindlist` now returns correct idcols for lists with different length vectors, [#3785](https://github.com/Rdatatable/data.table/issues/3785), [#3786](https://github.com/Rdatatable/data.table/pull/3786). Thanks to @shrektan for the report and fix.
 
+39. `DT[ , !rep(FALSE, ncol(DT)), with=FALSE]` correctly returns the full table, [#3013](https://github.com/Rdatatable/data.table/issues/3013) and [#2917](https://github.com/Rdatatable/data.table/issues/2917). Thanks @alexnss and @DavidArenburg for the reports.
+
 #### NOTES
 
 1. `rbindlist`'s `use.names="check"` now emits its message for automatic column names (`"V[0-9]+"`) too, [#3484](https://github.com/Rdatatable/data.table/pull/3484). See news item 5 of v1.12.2 below.
diff --git a/R/data.table.R b/R/data.table.R
index 790a6eb475..646fa15d6a 100644
--- a/R/data.table.R
+++ b/R/data.table.R
@@ -650,7 +650,7 @@ replace_dot_alias = function(e) {
         j = eval(jsub, lapply(substring(..syms,3L), get, pos=parent.frame()), parent.frame())
       }
       if (is.logical(j)) j <- which(j)
-      if (!length(j)) return( null.data.table() )
+      if (!length(j) && !notj) return( null.data.table() )
       if (is.factor(j)) j = as.character(j)  # fix for FR: #4867
       if (is.character(j)) {
         if (notj) {
@@ -680,7 +680,8 @@ replace_dot_alias = function(e) {
           if (any(j>0L)) stop("j mixes positives and negatives")
           j = seq_along(x)[j]  # all j are <0 here
         }
-        if (notj && length(j)) j = seq_along(x)[-j]
+        # 3013 -- handle !FALSE in column subset in j via logical+with
+        if (notj) j = seq_along(x)[if (length(j)) -j else TRUE]
         if (!length(j)) return(null.data.table())
         return(.Call(CsubsetDT, x, irows, j))
       } else {
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 1c6986b3f4..7da897e1c9 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -15984,6 +15984,10 @@ test(2102.1, cut(ID, breaks = br), as.IDate(cut(D, breaks=br)))
 test(2102.2, cut(ID, breaks = '1 year'), as.IDate(cut(D, breaks = '1 year')))
 test(2102.3, cut(ID, breaks = '6 months'), as.IDate(cut(D, breaks = '6 months')))
 
+# DT[ , !rep(FALSE, ncol(DT)), with=FALSE] would exit before doing !, #3013
+test(2103, DT[ , !rep(FALSE, 2L), with=FALSE], DT)
+
+
 ###################################
 #  Add new tests above this line  #
 ###################################