diff --git a/R/0_imports.R b/R/0_imports.R
index de3353c5..c7e4b448 100644
--- a/R/0_imports.R
+++ b/R/0_imports.R
@@ -47,7 +47,7 @@ utils::globalVariables(
     "rowwise", ".best", "location", "msg", "..object", ".eval_time",
     ".pred_survival", ".pred_time", ".weight_censored", "nice_time",
     "time_metric", ".lower", ".upper", "i", "results", "term", ".alpha",
-    ".method", "old_term"
+    ".method", "old_term", ".lab_pre", ".model", ".num_models"
   )
 )
 
diff --git a/R/grid_helpers.R b/R/grid_helpers.R
index 6fcad549..365386d5 100644
--- a/R/grid_helpers.R
+++ b/R/grid_helpers.R
@@ -318,50 +318,71 @@ compute_grid_info <- function(workflow, grid) {
 
   res <- min_grid(extract_spec_parsnip(workflow), grid)
 
+  syms_pre <- rlang::syms(parameters_preprocessor$id)
+  syms_mod <- rlang::syms(parameters_model$id)
+
+  # ----------------------------------------------------------------------------
+  # Create an order of execution to train the preprocessor (if any). This will
+  # define a loop over any preprocessing tuning parameter combinations.
   if (any_parameters_preprocessor) {
-    res$.iter_preprocessor <- seq_len(nrow(res))
+    pp_df <-
+      dplyr::distinct(res, !!!syms_pre) %>%
+      dplyr::arrange(!!!syms_pre) %>%
+      dplyr::mutate(
+        .iter_preprocessor = dplyr::row_number(),
+        .lab_pre = recipes::names0(max(dplyr::n()), "Preprocessor")
+      )
+    res <-
+      dplyr::full_join(res, pp_df, by = parameters_preprocessor$id) %>%
+      dplyr::arrange(.iter_preprocessor)
   } else {
     res$.iter_preprocessor <- 1L
+    res$.lab_pre <- "Preprocessor1"
   }
 
+  # Make the label shown in the grid and in loggining
   res$.msg_preprocessor <-
     new_msgs_preprocessor(
-      seq_len(max(res$.iter_preprocessor)),
+      res$.iter_preprocessor,
       max(res$.iter_preprocessor)
     )
 
-  if (nrow(res) != nrow(grid) ||
-      (any_parameters_model && !any_parameters_preprocessor)) {
-    res$.iter_model <- seq_len(dplyr::n_distinct(res[parameters_model$id]))
-  } else {
-    res$.iter_model <- 1L
-  }
-
-  res$.iter_config <- list(list())
-  for (row in seq_len(nrow(res))) {
-    res$.iter_config[row] <- list(iter_config(res[row, ]))
-  }
+  # ----------------------------------------------------------------------------
+  # Now make a similar iterator across models. Conditioning on each unique
+  # preprocessing candidate set, make an iterator for the model candidate sets
+  # (if any)
+
+  res <-
+    res %>%
+    dplyr::group_nest(.iter_preprocessor, keep = TRUE) %>%
+    dplyr::mutate(
+      .iter_config = purrr::map(data, make_iter_config),
+      .model = purrr::map(data, ~ tibble::tibble(.iter_model = seq_len(nrow(.x)))),
+      .num_models = purrr::map_int(.model, nrow)
+    ) %>%
+    dplyr::select(-.iter_preprocessor) %>%
+    tidyr::unnest(cols = c(data, .model, .iter_config)) %>%
+    dplyr::select(-.lab_pre) %>%
+    dplyr::relocate(dplyr::starts_with(".iter"))
 
   res$.msg_model <-
-    new_msgs_model(i = res$.iter_model, n = max(res$.iter_model), res$.msg_preprocessor)
+    new_msgs_model(i = res$.iter_model,
+                   n = res$.num_models,
+                   res$.msg_preprocessor)
 
-  res
+  res %>%
+    dplyr::select(-.num_models) %>%
+    dplyr::relocate(dplyr::starts_with(".msg"))
 }
 
-iter_config <- function(res_row) {
-  submodels <- res_row$.submodels[[1]]
-  if (identical(submodels, list())) {
-    models <- res_row$.iter_model
-  } else {
-    models <- seq_len(length(submodels[[1]]) + 1)
-  }
-
-  paste0(
-    "Preprocessor",
-    res_row$.iter_preprocessor,
-    "_Model",
-    format_with_padding(models)
-  )
+make_iter_config <- function(dat) {
+  # Compute labels for the models *within* each preprocessing loop.
+  num_submodels <- purrr::map_int(dat$.submodels, ~ length(unlist(.x)))
+  num_models <- sum(num_submodels + 1) # +1 for the model being trained
+  .mod_label <- recipes::names0(num_models, "Model")
+  .iter_config <- paste(dat$.lab_pre[1], .mod_label, sep = "_")
+  .iter_config <- vctrs::vec_chop(.iter_config, sizes = num_submodels + 1)
+  tibble::tibble(.iter_config  = .iter_config)
 }
 
 # This generates a "dummy" grid_info object that has the same
diff --git a/tests/testthat/_snaps/checks.md b/tests/testthat/_snaps/checks.md
index 94524b2d..d98ea891 100644
--- a/tests/testthat/_snaps/checks.md
+++ b/tests/testthat/_snaps/checks.md
@@ -92,6 +92,22 @@
       Error in `tune:::check_workflow()`:
       ! A parsnip model is required.
 
+# errors informatively when needed package isn't installed
+
+    Code
+      check_workflow(stan_wflow)
+    Condition
+      Error:
+      ! Package install is required for rstanarm.
+
+---
+
+    Code
+      fit_resamples(stan_wflow, rsample::bootstraps(mtcars))
+    Condition
+      Error in `fit_resamples()`:
+      ! Package install is required for rstanarm.
+
 # workflow objects (will not tune, tidymodels/tune#548)
 
     Code
diff --git a/tests/testthat/_snaps/grid.md b/tests/testthat/_snaps/grid.md
index 4f64bce4..a975cfb4 100644
--- a/tests/testthat/_snaps/grid.md
+++ b/tests/testthat/_snaps/grid.md
@@ -8,12 +8,12 @@
     Message
       x Fold1: preprocessor 1/1:
         Error in `step_spline_b()`:
-        Caused by error in `spline_msg()`:
-        ! Error in if (df < 0)  : missing value where TRUE/FALSE needed
+        Caused by error in `prep()`:
+        ! `deg_free` must be a whole number, not a numeric `NA`.
       x Fold2: preprocessor 1/1:
         Error in `step_spline_b()`:
-        Caused by error in `spline_msg()`:
-        ! Error in if (df < 0)  : missing value where TRUE/FALSE needed
+        Caused by error in `prep()`:
+        ! `deg_free` must be a whole number, not a numeric `NA`.
     Condition
       Warning:
       All models failed. Run `show_notes(.Last.tune.result)` for more information.
@@ -28,10 +28,10 @@
     Message
       x Fold1: preprocessor 1/1:
         Error in `get_all_predictors()`:
-        ! The following predictors were not found in `data`: 'z'.
+        ! The following predictor was not found in `data`: "z".
       x Fold2: preprocessor 1/1:
         Error in `get_all_predictors()`:
-        ! The following predictors were not found in `data`: 'z'.
+        ! The following predictor was not found in `data`: "z".
     Condition
       Warning:
       All models failed. Run `show_notes(.Last.tune.result)` for more information.
diff --git a/tests/testthat/_snaps/resample.md b/tests/testthat/_snaps/resample.md
index e768f80c..9fc0e154 100644
--- a/tests/testthat/_snaps/resample.md
+++ b/tests/testthat/_snaps/resample.md
@@ -5,12 +5,12 @@
     Message
       x Fold1: preprocessor 1/1:
         Error in `step_spline_natural()`:
-        Caused by error in `spline_msg()`:
-        ! Error in if (df < 2)  : missing value where TRUE/FALSE needed
+        Caused by error in `prep()`:
+        ! `deg_free` must be a whole number, not a numeric `NA`.
       x Fold2: preprocessor 1/1:
         Error in `step_spline_natural()`:
-        Caused by error in `spline_msg()`:
-        ! Error in if (df < 2)  : missing value where TRUE/FALSE needed
+        Caused by error in `prep()`:
+        ! `deg_free` must be a whole number, not a numeric `NA`.
     Condition
       Warning:
       All models failed. Run `show_notes(.Last.tune.result)` for more information.
@@ -20,7 +20,7 @@
     Code
       note
     Output
-      [1] "Error in `step_spline_natural()`:\nCaused by error in `spline_msg()`:\n! Error in if (df < 2) { : missing value where TRUE/FALSE needed"
+      [1] "Error in `step_spline_natural()`:\nCaused by error in `prep()`:\n! `deg_free` must be a whole number, not a numeric `NA`."
 
 # failure in variables tidyselect specification is caught elegantly
 
diff --git a/tests/testthat/test-grid_helpers.R b/tests/testthat/test-grid_helpers.R
index e0acfe1a..dff242c9 100644
--- a/tests/testthat/test-grid_helpers.R
+++ b/tests/testthat/test-grid_helpers.R
@@ -15,7 +15,7 @@ test_that("compute_grid_info - recipe only", {
 
   expect_equal(res$.iter_preprocessor, 1:5)
   expect_equal(res$.msg_preprocessor, paste0("preprocessor ", 1:5, "/5"))
-  expect_equal(res$deg_free, grid$deg_free)
+  expect_equal(sort(res$deg_free), sort(grid$deg_free))
   expect_equal(res$.iter_model, rep(1, 5))
   expect_equal(res$.iter_config, as.list(paste0("Preprocessor", 1:5, "_Model1")))
   expect_equal(res$.msg_model, paste0("preprocessor ", 1:5, "/5, model 1/1"))
@@ -27,6 +27,7 @@ test_that("compute_grid_info - recipe only", {
     ignore.order = TRUE
   )
   expect_equal(nrow(res), 5)
+  expect_equal(vctrs::vec_unique_count(res$.iter_config), nrow(grid))
 })
 
 test_that("compute_grid_info - model only (no submodels)", {
@@ -57,6 +58,7 @@ test_that("compute_grid_info - model only (no submodels)", {
     ignore.order = TRUE
   )
   expect_equal(nrow(res), 5)
+  expect_equal(vctrs::vec_unique_count(res$.iter_config), nrow(grid))
 })
 
 test_that("compute_grid_info - model only (with submodels)", {
@@ -107,8 +109,8 @@ test_that("compute_grid_info - recipe and model (no submodels)", {
 
   expect_equal(res$.iter_preprocessor, 1:5)
   expect_equal(res$.msg_preprocessor, paste0("preprocessor ", 1:5, "/5"))
-  expect_equal(res$learn_rate, grid$learn_rate)
-  expect_equal(res$deg_free, grid$deg_free)
+  expect_equal(sort(res$learn_rate), sort(grid$learn_rate))
+  expect_equal(sort(res$deg_free), sort(grid$deg_free))
   expect_equal(res$.iter_model, rep(1, 5))
   expect_equal(res$.iter_config, as.list(paste0("Preprocessor", 1:5, "_Model1")))
   expect_equal(res$.msg_model, paste0("preprocessor ", 1:5, "/5, model 1/1"))
@@ -120,6 +122,7 @@ test_that("compute_grid_info - recipe and model (no submodels)", {
     ignore.order = TRUE
   )
   expect_equal(nrow(res), 5)
+  expect_equal(vctrs::vec_unique_count(res$.iter_config), nrow(grid))
 })
 
 test_that("compute_grid_info - recipe and model (with submodels)", {
@@ -169,6 +172,7 @@ test_that("compute_grid_info - recipe and model (with submodels)", {
   )
   expect_equal(nrow(res), 3)
 })
+
 test_that("compute_grid_info - recipe and model (with and without submodels)", {
   library(workflows)
   library(parsnip)
@@ -185,7 +189,9 @@ test_that("compute_grid_info - recipe and model (with and without submodels)", {
   # use grid_regular to (partially) trigger submodel trick
   set.seed(1)
   param_set <- extract_parameter_set_dials(wflow)
-  grid <- bind_rows(grid_regular(param_set), grid_space_filling(param_set))
+  grid <-
+    bind_rows(grid_regular(param_set), grid_space_filling(param_set)) %>%
+    arrange(deg_free, loss_reduction, trees)
   res <- compute_grid_info(wflow, grid)
 
   expect_equal(length(unique(res$.iter_preprocessor)), 5)
@@ -193,17 +199,20 @@ test_that("compute_grid_info - recipe and model (with and without submodels)", {
     unique(res$.msg_preprocessor),
     paste0("preprocessor ", 1:5, "/5")
   )
-  expect_equal(res$trees, c(rep(max(grid$trees), 10), 1))
+  expect_equal(sort(res$trees), sort(c(rep(max(grid$trees), 10), 1)))
   expect_equal(unique(res$.iter_model), 1:3)
   expect_equal(
-    res$.iter_config[1:3],
+    res$.iter_config[res$.iter_preprocessor == 1],
     list(
-      c("Preprocessor1_Model1", "Preprocessor1_Model2", "Preprocessor1_Model3", "Preprocessor1_Model4"),
-      c("Preprocessor2_Model1", "Preprocessor2_Model2", "Preprocessor2_Model3"),
-      c("Preprocessor3_Model1", "Preprocessor3_Model2", "Preprocessor3_Model3")
+      c("Preprocessor1_Model01", "Preprocessor1_Model02", "Preprocessor1_Model03", "Preprocessor1_Model04"),
+      c("Preprocessor1_Model05", "Preprocessor1_Model06", "Preprocessor1_Model07"),
+      c("Preprocessor1_Model08", "Preprocessor1_Model09", "Preprocessor1_Model10")
     )
   )
-  expect_equal(res$.msg_model[1:3], paste0("preprocessor ", 1:3, "/5, model 1/3"))
+  expect_equal(
+    res$.msg_model[res$.iter_preprocessor == 1],
+    paste0("preprocessor 1/5, model ", 1:3, "/3")
+  )
   expect_equal(
     res$.submodels[1:3],
     list(
@@ -212,6 +221,12 @@ test_that("compute_grid_info - recipe and model (with and without submodels)", {
       list(trees = c(1L, 1000L))
     )
   )
+  expect_equal(
+    res %>%
+      mutate(num_models = purrr::map_int(.iter_config, length)) %>%
+      summarize(n = sum(num_models), .by = c(deg_free)),
+    grid %>% count(deg_free)
+  )
   expect_named(
     res,
     c(".iter_preprocessor", ".msg_preprocessor", "deg_free", "trees",
@@ -325,4 +340,5 @@ test_that("compute_grid_info - recipe and model (no submodels but has inner grid
     ignore.order = TRUE
   )
   expect_equal(nrow(res), 9)
+  expect_equal(vctrs::vec_unique_count(res$.iter_config), nrow(grid))
 })