diff --git a/NAMESPACE b/NAMESPACE
index 361b706d3..9d5ff618c 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -75,7 +75,7 @@ export(fctr)
 S3method("[", data.table)
 S3method("[<-", data.table)
 # S3method("[[", data.table)
-# S3method("[[<-", data.table)
+S3method("[[<-", data.table)
 S3method("$<-", data.table)
 S3method(print, data.table)
 S3method(as.data.table, data.table)
diff --git a/NEWS.md b/NEWS.md
index 4a821991b..df2437cd6 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -346,6 +346,8 @@ See [#2611](https://github.com/Rdatatable/data.table/issues/2611) for details. T
 
 23. `fread()` auto-detects separators for single-column files consisting solely of quoted values (e.g. `"this_that"\n"2025-01-01 00:00:01"`), [#7366](https://github.com/Rdatatable/data.table/issues/7366). Thanks @arunsrinivasan for the report and @ben-schwen for the fix.
 
+24. Assigning via `[[<-` now changes data.tables by reference, so forms like `DT[["col"]] = value` or `DT[[1, "col"]] = value` keep over-allocation intact instead of falling back to the data.frame method, [#6734](https://github.com/Rdatatable/data.table/issues/6734). Thanks @mb706 for the report and @ben-schwen for the implementation.
+
 ### NOTES
 
 1. The following in-progress deprecations have proceeded:
diff --git a/R/as.data.table.R b/R/as.data.table.R
index f849aa8c1..677e72189 100644
--- a/R/as.data.table.R
+++ b/R/as.data.table.R
@@ -141,6 +141,12 @@ as.data.table.list = function(x,
   rownames_ = NULL
   check_rownames = !isFALSE(keep.rownames)
 
+  # conversion must happen after capturing names
+  if (is.data.table(x)) {
+    # operate on plain list to avoid [[<-.data.table dispatch
+    x = as.list(x)
+  }
+
   for (i in seq_len(n)) {
     xi = x[[i]]
     if (is.null(xi)) next    # eachncol already initialized to 0 by integer() above
diff --git a/R/data.table.R b/R/data.table.R
index db74384c4..9e6735782 100644
--- a/R/data.table.R
+++ b/R/data.table.R
@@ -2308,6 +2308,23 @@ tail.data.table = function(x, n=6L, ...) {
   set(x,j=name,value=value)  # important i is missing here
 }
 
+"[[<-.data.table" = function(x, i, j, value) {
+  n = nargs()
+  if (!cedta()) {
+    # nocov start
+    ans = if (n<4L) `[<-.data.frame`(x, i, value=value)
+          else `[<-.data.frame`(x, i, j, value)
+    return(setalloccol(ans))           # over-allocate (again)
+    # nocov end
+  }
+  x = copy(x)
+  if (n<4L) {
+    set(x, j=i, value=value)
+  } else {
+    set(x, i, j, value)
+  }
+}
+
 as.data.frame.data.table = function(x, row.names = NULL, ...)
 {
   ans = setDF(copy(x), rownames = row.names) # issue #5319
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index e6ef9be1d..c6d622797 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -1405,10 +1405,18 @@ test(437.2, truelength(DT), 2044L)
 DT = data.table(a=1:3,b=4:6)
 tl = truelength(DT)
 DT$foo = 7L
-test(438, truelength(DT), tl)
+test(438.1, truelength(DT), tl)
 DT[,"bar"] = 8L
-test(439, truelength(DT), tl+2L)
-test(440, DT, data.table(a=1:3,b=4:6,foo=7L,bar=8L))
+test(438.2, truelength(DT), tl+2L)
+# also allow DT[[...]]= syntax #6734
+DT[["baz"]] = 1L
+test(438.3, truelength(DT), tl+2L)
+test(438.4, DT$baz, c(1L,1L,1L))
+DT[[5]] = 9L
+test(438.5, truelength(DT), tl+3L)
+DT[[1,"qux"]] = 10L
+test(438.6, truelength(DT), tl+3L)
+test(438.7, DT, data.table(a=1:3,b=4:6,foo=7L,bar=8L,baz=9L,qux=c(10L,NA_integer_,NA_integer_)))
 
 # Test rbind works by colname now, for consistency with base, FR#1634
 DT = data.table(a=1:3,b=4:6)
@@ -4089,6 +4097,8 @@ test(1140, as.data.table(X), data.table(a=c(1:2,1L), b=c(1:3)),
 test(1141.1, data.table(a=1:2, b=1:3), data.table(a=c(1L,2L,1L), b=1:3),                                              warning="Item 1 has 2 rows but longest item has 3; recycled")
 test(1141.2, data.table(a=1:2, data.table(x=1:5, y=6:10)), data.table(a=c(1L,2L,1L,2L,1L), x=1:5, y=6:10),            warning="Item 1 has 2 rows but longest item has 5; recycled")
 test(1141.3, data.table(a=1:5, data.table(x=c(1,2), y=c(3,4))), data.table(a=c(1:5), x=c(1,2,1,2,1), y=c(3,4,3,4,3)), warning="Item 2 has 2 rows but longest item has 5; recycled")
+x = structure(list(1, 2), class = c("list", "data.table"))
+test(1141.4, as.data.table(x), data.table(V1=c(1), V2=c(2)))
 
 # Fix for bug #79 - DT[, foo()] returns function definition.
 DT <- data.table(a=1:2)