diff --git a/R/data.table.R b/R/data.table.R
index bdc92e0aa..f05220a62 100644
--- a/R/data.table.R
+++ b/R/data.table.R
@@ -2862,6 +2862,9 @@ set = function(x,i=NULL,j,value)  # low overhead, loopable
     setalloccol(x, verbose=FALSE)
     if (is.name(name)) {
       assign(as.character(name), x, parent.frame(), inherits=TRUE)
+    } else if (is.call(name)) {
+      # handle subexpressions like self$dt, foo[["bar"]], etc. by evaluating the assignment in parent frame
+      eval(call("<-", name, x), parent.frame())
     }
   }
   .Call(Cassign,x,i,j,NULL,value)
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index b9d9a3ba5..53b7ea898 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -21906,7 +21906,13 @@ null_in_value <- NULL
 test(2351.3, "cyl" %notin% names(DT[, cyl := null_in_value]))
 DT = unserialize(serialize(as.data.table(mtcars), NULL))
 test(2351.4,  ncol(DT[, c("cyl", "mpg") := .(null_in_value, null_in_value)]), ncol(mtcars) - 2L)
-rm(DT)
+l = list(DT = unserialize(serialize(as.data.table(mtcars), NULL)))
+test(2351.5, set(l$DT, j="carb", value=NULL), as.data.table(mtcars)[,carb:=NULL])
+test(2351.6, "carb" %notin% names(l$DT))
+l = list(DT = unserialize(serialize(as.data.table(mtcars), NULL)))
+test(2351.7, set(l[["DT"]], j="carb", value=NULL), as.data.table(mtcars)[,carb:=NULL])
+test(2351.8, "carb" %notin% names(l$DT))
+rm(DT, l)
 
 # rbindlist did not protect the temporary UTF-8 strings, #7452
 DTn = apply(matrix(as.raw(rep(0xa1:0xff, length.out = 100)), 10), 2, rawToChar)