diff --git a/R/surveyFA.R b/R/surveyFA.R
index f60fffd8..fe4306f4 100644
--- a/R/surveyFA.R
+++ b/R/surveyFA.R
@@ -1,3 +1,20 @@
+#' Select the first named minimum without sorting the full vector
+#'
+#' @description Returns the name attached to the first minimum value in a named
+#'   numeric vector. The helper intentionally uses a single linear scan so the
+#'   bounded recovery loop does not pay the cost of sorting every candidate.
+#' @param values A named numeric vector whose missing-value policy has already
+#'   been applied by the caller.
+#' @return The first minimum value's name, or `NA_character_` for an empty input.
+#' @keywords internal
+.minimum_named_value <- function(values) {
+  minimum_index <- which.min(values)
+  if (length(minimum_index) == 0L) {
+    return(NA_character_)
+  }
+  names(values)[minimum_index]
+}
+
 #' @title surveyFA
 #' @description Fallback calibration helper used when direct model estimation in
 #'   `autoFIPC()` fails.
@@ -232,7 +249,7 @@ surveyFA <- function(
       names(p_values) <- rownames(fit_df)
       if (any(!is.na(p_values))) {
         p_values[is.na(p_values)] <- 1
-        candidate <- names(sort(p_values, decreasing = FALSE))[1L]
+        candidate <- .minimum_named_value(p_values)
         if (!is.na(candidate) && p_values[[candidate]] < pThreshold) {
           return(candidate)
         }
diff --git a/tests/testthat/test-surveyFA.R b/tests/testthat/test-surveyFA.R
index 060ae68e..9ed1c425 100644
--- a/tests/testthat/test-surveyFA.R
+++ b/tests/testthat/test-surveyFA.R
@@ -58,8 +58,32 @@ test_that("surveyFA validates boolean control flags before estimator dispatch",
   )
 })
 
+test_that("minimum named selection preserves prior sort semantics", {
+  normalized_cases <- list(
+    c(item_a = 0.40, item_b = 0.10, item_c = 0.30),
+    c(item_a = 0.10, item_b = 0.10, item_c = 0.20),
+    c(item_a = -0.50, item_b = 0.00, item_c = 0.50)
+  )
+  missing_case <- c(item_a = NA_real_, item_b = 0.20, item_c = 0.30)
+  missing_case[is.na(missing_case)] <- 1
+  normalized_cases[[length(normalized_cases) + 1L]] <- missing_case
+
+  for (p_values in normalized_cases) {
+    prior_candidate <- names(sort(p_values, decreasing = FALSE))[1L]
+    expect_identical(
+      aFIPC:::.minimum_named_value(p_values),
+      prior_candidate
+    )
+  }
+  expect_identical(
+    aFIPC:::.minimum_named_value(setNames(numeric(), character())),
+    NA_character_
+  )
+})
+
 test_that("surveyFA reports bounded recovery exhaustion when unrecoverable", {
   skip_if_not_installed("mirt")
+  set.seed(20260726)
 
   raw <- as.data.frame(
     matrix(