diff --git a/NEWS.md b/NEWS.md
index 2cc4948b..e5df0850 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,10 @@
 # tune (development version)
 
+* Iterative searches now cache preprocessor fits that would be duplicated across
+  iterations, greatly reducing the time to tune computationally intensive
+  preprocessing steps in `tune_bayes()` (and `tune_sim_anneal()`) in 
+  finetune (#955).
+
 * The package will now warn when parallel processing has been enabled with foreach but not with future. See [`?parallelism`](https://tune.tidymodels.org/dev/reference/parallelism.html) to learn more about transitioning your code to future (#878, #866).
 
 * The package will now log a backtrace for errors and warnings that occur during tuning. When a tuning process encounters issues, see the new `trace` column in the `collect_notes(.Last.tune.result)` output to find precisely where the error occurred (#873).
diff --git a/R/cache.R b/R/cache.R
new file mode 100644
index 00000000..37f223a6
--- /dev/null
+++ b/R/cache.R
@@ -0,0 +1,32 @@
+# For iterative searches, the same preprocessor fits are recomputed
+# for every iteration. Hook into the `tune_env`, an environment that
+# defines a call to a tuning function, to cache repeated fits while tuning.
+has_cached_result <- function(split_id, param_desc) {
+  cache <- cached_results()
+
+  if (!split_id %in% names(cache) || !param_desc %in% names(cache[[split_id]])) {
+    return(FALSE)
+  }
+
+  TRUE
+}
+
+get_cached_result <- function(split_id, param_desc) {
+  cache <- cached_results()
+  cache[[split_id]][[param_desc]]
+}
+
+set_cached_result <- function(split_id, param_desc, workflow) {
+  cache <- cached_results()
+  cache[[split_id]][[param_desc]] <- workflow
+  workflow
+}
+
+cached_results <- function() {
+  env <- tune_env$progress_env
+  if (!"cache" %in% names(env)) {
+    rlang::env_bind(env, cache = rlang::new_environment())
+  }
+
+  env$cache
+}
diff --git a/R/grid_code_paths.R b/R/grid_code_paths.R
index 505d6ccc..7082fe45 100644
--- a/R/grid_code_paths.R
+++ b/R/grid_code_paths.R
@@ -436,13 +436,19 @@ tune_grid_loop_iter <- function(split,
       grid_preprocessor = iter_grid_preprocessor
     )
 
-    workflow <- .catch_and_log(
-      .expr = .fit_pre(workflow, analysis),
-      control,
-      split_labels,
-      iter_msg_preprocessor,
-      notes = out_notes
-    )
+    if (!has_cached_result(split_labels$id, iter_msg_preprocessor)) {
+      workflow <- .catch_and_log(
+        .expr = .fit_pre(workflow, analysis),
+        control,
+        split_labels,
+        iter_msg_preprocessor,
+        notes = out_notes
+      )
+
+      set_cached_result(split_labels$id, iter_msg_preprocessor, workflow)
+    } else {
+      workflow <- get_cached_result(split_labels$id, iter_msg_preprocessor)
+    }
 
     if (is_failure(workflow)) {
       next