diff --git a/NEWS.md b/NEWS.md
index a51eb4fe9..cb198fa7c 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,9 @@
 # dbplyr (development version)
 
+* Refined the `select()` inlining criteria to keep computed columns used to
+  `arrange()` subqueries that are eliminated by a subsequent select (@ejneer,
+  #1437).
+
 * dbplyr now exports some tools to work with the internal `table_path` class
   which is useful for certain backends that need to work with this 
   data structure (#1300).
diff --git a/R/verb-select.R b/R/verb-select.R
index c1ee020a2..ef93594f3 100644
--- a/R/verb-select.R
+++ b/R/verb-select.R
@@ -114,7 +114,7 @@ add_select <- function(lazy_query, vars) {
   }
 
   is_select <- is_lazy_select_query(lazy_query)
-  select_can_be_inlined <- is_bijective_projection(vars, vars_data) || !is_true(lazy_query$distinct)
+  select_can_be_inlined <- select_can_be_inlined(lazy_query, vars)
   if (is_select && select_can_be_inlined) {
     idx <- vctrs::vec_match(vars, vars_data)
 
@@ -131,9 +131,20 @@ add_select <- function(lazy_query, vars) {
   )
 }
 
-is_bijective_projection <- function(vars, names_prev) {
-  vars <- unname(vars)
-  identical(sort(vars), names_prev)
+select_can_be_inlined <- function(lazy_query, vars) {
+  # all computed columns used for ordering (if any) must be present
+  computed_flag <- purrr::map_lgl(lazy_query$select$expr, is_quosure)
+  computed_columns <- lazy_query$select$name[computed_flag]
+
+  order_vars <- purrr::map_chr(lazy_query$order_by, as_label)
+  ordered_present <- all(intersect(computed_columns, order_vars) %in% vars)
+
+  # if the projection is distinct, it must be bijective
+  is_distinct <- is_true(lazy_query$distinct)
+  is_bijective_projection <- identical(sort(unname(vars)), op_vars(lazy_query))
+  distinct_is_bijective <- !is_distinct || is_bijective_projection
+
+  ordered_present && distinct_is_bijective
 }
 
 rename_groups <- function(lazy_query, vars) {
diff --git a/tests/testthat/_snaps/verb-select.md b/tests/testthat/_snaps/verb-select.md
index 0140cc721..327a24e67 100644
--- a/tests/testthat/_snaps/verb-select.md
+++ b/tests/testthat/_snaps/verb-select.md
@@ -181,6 +181,22 @@
       Error in `select()`:
       ! This tidyselect interface doesn't support predicates.
 
+# arranged computed columns are not inlined away
+
+    Code
+      lf %>% mutate(z = 1) %>% arrange(x, z) %>% select(x)
+    Condition
+      Warning:
+      ORDER BY is ignored in subqueries without LIMIT
+      i Do you need to move arrange() later in the pipeline or use window_order() instead?
+    Output
+      <SQL>
+      SELECT `x`
+      FROM (
+        SELECT `df`.*, 1.0 AS `z`
+        FROM `df`
+      ) AS `q01`
+
 # multiple selects are collapsed
 
     Code
diff --git a/tests/testthat/test-verb-select.R b/tests/testthat/test-verb-select.R
index 62e567769..bebe74429 100644
--- a/tests/testthat/test-verb-select.R
+++ b/tests/testthat/test-verb-select.R
@@ -35,6 +35,31 @@ test_that("select after distinct produces subquery", {
   expect_true(lq$x$distinct)
 })
 
+test_that("select after arrange produces subquery, if needed", {
+  lf <- lazy_frame(x = 1)
+
+  # shouldn't inline
+  out <- lf %>% mutate(z = 2) %>% arrange(x, z) %>% select(x)
+  # should inline
+  out2 <- lf %>% mutate(z = 2) %>% arrange(x, z) %>% select(x, z)
+
+  inner_query <- out$lazy_query$x
+  expect_s3_class(inner_query, "lazy_select_query")
+  expect_equal(inner_query$order_by, list(quo(x), quo(z)), ignore_formula_env = TRUE)
+  expect_equal(
+    op_vars(inner_query),
+    c("x", "z")
+  )
+  expect_equal(op_vars(out$lazy_query), "x")
+
+  # order vars in a subquery are dropped
+  expect_equal(
+    inner_query[setdiff(names(inner_query), "order_vars")],
+    out2$lazy_query[setdiff(names(out2$lazy_query), "order_vars")]
+  )
+})
+
+
 test_that("rename/relocate after distinct is inlined #1141", {
   lf <- lazy_frame(x = 1, y = 1:2)
   expect_snapshot({
@@ -284,6 +309,33 @@ test_that("where() isn't suppored", {
   })
 })
 
+test_that("arranged computed columns are not inlined away", {
+  lf <- lazy_frame(x = 1)
+
+  # shouldn't inline
+  out <- lf %>% mutate(z = 2) %>% arrange(x, z) %>% select(x)
+  # should inline
+  out2 <- lf %>% mutate(z = 2) %>% arrange(x, z) %>% select(x, z)
+
+  inner_query <- out$lazy_query$x
+  expect_snapshot({
+      lf %>% mutate(z = 1) %>% arrange(x, z) %>% select(x)
+  })
+  expect_s3_class(inner_query, "lazy_select_query")
+  expect_equal(
+    inner_query$order_by,
+    list(quo(x), quo(z)),
+    ignore_formula_env = TRUE
+  )
+  expect_equal(op_vars(inner_query), c("x", "z"))
+  expect_equal(op_vars(out$lazy_query), "x")
+  expect_equal(
+      # order vars in a subquery are dropped
+      inner_query[setdiff(names(inner_query), "order_vars")],
+      out2$lazy_query[setdiff(names(out2$lazy_query), "order_vars")]
+  )
+})
+
 # sql_render --------------------------------------------------------------
 
 test_that("multiple selects are collapsed", {