diff --git a/R/install.R b/R/install.R
index ee91fd1c..94764001 100644
--- a/R/install.R
+++ b/R/install.R
@@ -804,14 +804,15 @@ rtools4x_toolchain_path <- function() {
 
 rtools4x_version <- function() {
   rtools_ver <- NULL
+  r_version <- current_r_version()
 
-  if (R.version$minor < "2.0") {
+  if (r_version < "4.2.0") {
     rtools_ver <- "40"
-  } else if (R.version$minor < "3.0") {
+  } else if (r_version < "4.3.0") {
     rtools_ver <- "42"
-  } else if (R.version$minor < "4.0") {
+  } else if (r_version < "4.4.0") {
     rtools_ver <- "43"
-  } else if (R.version$minor < "5.0") {
+  } else if (r_version < "4.5.0") {
     rtools_ver <- "44"
   } else {
     rtools_ver <- "45"
diff --git a/R/model.R b/R/model.R
index 0359678a..25b49ba4 100644
--- a/R/model.R
+++ b/R/model.R
@@ -1138,7 +1138,8 @@ sample <- function(data = NULL,
                    save_metric = getOption("cmdstanr_save_metric", FALSE),
                    save_cmdstan_config = getOption("cmdstanr_save_config", FALSE)) {
 
-  if (self$cmdstan_version() < "2.36.0" && !fixed_param) {
+  if (cmdstan_version_compare(self$cmdstan_version(), "2.36.0") < 0 &&
+      !fixed_param) {
     if (self$has_stan_file() && file.exists(self$stan_file())) {
       if (!is.null(self$variables()) && length(self$variables()$parameters) == 0) {
         stop("Model contains no parameters. Please use 'fixed_param = TRUE'.", call. = FALSE)
@@ -2570,4 +2571,3 @@ map_cmdstan_to_cmdstanr <- function(method) {
          character(0)
   )
 }
-
diff --git a/R/path.R b/R/path.R
index a62c233e..b06ccfd1 100644
--- a/R/path.R
+++ b/R/path.R
@@ -134,12 +134,35 @@ cmdstan_min_version <- function() {
   "2.35.0"
 }
 
-is_supported_cmdstan_version <- function(version) {
-  if (is.null(version)) {
-    return(FALSE)
+# Normalize versions for comparison. This is intentionally looser than
+# cmdstan_version_from_path(): it accepts version strings, paths, and install
+# dir names, and strips release-candidate suffixes.
+cmdstan_version_for_comparison <- function(version) {
+  version <- as.character(version)
+  version <- sub("[/\\\\]+$", "", version)
+  version <- basename(version)
+  version <- sub("^cmdstan-", "", version)
+  sub("-rc[0-9]+$", "", version)
+}
+
+# Scalar comparison of versions numbers. Returns -1, 0, or 1.
+# Empty strings are used when no native or WSL install was found during path discovery.
+cmdstan_version_compare <- function(version, other) {
+  if (length(version) != 1 || is.na(version) || !nzchar(version)) {
+    return(-1L)
   }
+  if (length(other) != 1 || is.na(other) || !nzchar(other)) {
+    return(1L)
+  }
+  utils::compareVersion(
+    cmdstan_version_for_comparison(version),
+    cmdstan_version_for_comparison(other)
+  )
+}
+
+is_supported_cmdstan_version <- function(version) {
   cmp <- tryCatch(
-    suppressWarnings(utils::compareVersion(as.character(version), cmdstan_min_version())),
+    suppressWarnings(cmdstan_version_compare(version, cmdstan_min_version())),
     error = function(e) NA_integer_
   )
   isTRUE(cmp >= 0)
@@ -241,7 +264,7 @@ cmdstan_default_path <- function(dir = NULL) {
     if (!nzchar(latest_cmdstan) && !nzchar(latest_wsl_cmdstan)) {
       return(NULL)
     }
-    if (latest_wsl_cmdstan >= latest_cmdstan) {
+    if (cmdstan_version_compare(latest_wsl_cmdstan, latest_cmdstan) >= 0) {
       return(file.path(wsl_installs_path, latest_wsl_cmdstan))
     } else {
       return(file.path(installs_path, latest_cmdstan))
@@ -250,15 +273,26 @@ cmdstan_default_path <- function(dir = NULL) {
   NULL
 }
 
+# Return the newest CmdStan install directory name under an install root
 latest_cmdstan_installed <- function(installs_path) {
   cmdstan_installs <- list.dirs(path = installs_path, recursive = FALSE, full.names = FALSE)
   latest_cmdstan <- ""
   if (length(cmdstan_installs) > 0) {
-    cmdstan_installs <- grep("^cmdstan-", cmdstan_installs, value = TRUE)
+    cmdstan_installs <- grep(
+      "^cmdstan-[0-9]+\\.[0-9]+\\.[0-9]+(-rc[0-9]+)?$",
+      cmdstan_installs,
+      value = TRUE
+    )
     if (length(cmdstan_installs) == 0) {
       return(latest_cmdstan)
     }
-    latest_cmdstan <- sort(cmdstan_installs, decreasing = TRUE)[1]
+    # list.dirs() returns dir names, so sort by parsed versions instead of
+    # lexicographic names
+    latest_cmdstan <- cmdstan_installs[order(
+      numeric_version(cmdstan_version_for_comparison(cmdstan_installs)),
+      cmdstan_installs,
+      decreasing = TRUE
+    )[1]]
     if (is_release_candidate(latest_cmdstan)) {
       non_rc_path <- strsplit(latest_cmdstan, "-rc")[[1]][1]
       if (dir.exists(file.path(installs_path, non_rc_path))) {
@@ -269,6 +303,7 @@ latest_cmdstan_installed <- function(installs_path) {
   latest_cmdstan
 }
 
+# Detect WSL UNC paths, which may need path-based version fallback below
 is_wsl_unc_path <- function(path) {
   is.character(path) &&
     length(path) == 1 &&
@@ -276,6 +311,9 @@ is_wsl_unc_path <- function(path) {
     startsWith(repair_path(path), "//wsl$/")
 }
 
+# Strict extractor for CmdStan install paths. Unlike
+# cmdstan_version_for_comparison(), it returns NULL for non-CmdStan paths and
+# preserves release-candidate suffixes.
 cmdstan_version_from_path <- function(path) {
   path <- repair_path(path)
   match <- regmatches(
diff --git a/R/run.R b/R/run.R
index eefa6d7c..8a15bf49 100644
--- a/R/run.R
+++ b/R/run.R
@@ -67,11 +67,11 @@ CmdStanRun <- R6::R6Class(
       self$args$new_files(type = "profile")
     },
     new_config_files = function() {
-      # because CmdStan 2.34 uses the output_file name as the base for the config file
+      # the output_file name is used as the base for the config file
       paste0(tools::file_path_sans_ext(private$output_files_), "_config.json")
     },
     new_metric_files = function() {
-      # because CmdStan 2.34 uses the output_file name as the base for the metric file
+      # the output_file name is used as the base for the metric file
       paste0(tools::file_path_sans_ext(private$output_files_), "_metric.json")
     },
     config_files = function(include_failed = FALSE) {
diff --git a/R/utils.R b/R/utils.R
index 40fa62c3..4b925549 100644
--- a/R/utils.R
+++ b/R/utils.R
@@ -58,8 +58,13 @@ os_is_linux <- function() {
   isTRUE(Sys.info()[["sysname"]] == "Linux")
 }
 
+current_r_version <- function() {
+  getRversion()
+}
+
 is_ucrt_toolchain <- function() {
-  os_is_windows() && R.version$major == "4" && R.version$minor >= "2.0"
+  r_version <- current_r_version()
+  os_is_windows() && r_version >= "4.2.0" && r_version < "5.0.0"
 }
 
 # Check if running R in Rosetta 2 translation environment, which is an
diff --git a/R/zzz.R b/R/zzz.R
index bea367db..0ea38313 100644
--- a/R/zzz.R
+++ b/R/zzz.R
@@ -25,7 +25,7 @@ startup_messages <- function() {
     current_version <- try(cmdstan_version(), silent = TRUE)
     if (!inherits(latest_version, "try-error")
         && !inherits(current_version, "try-error")
-        && latest_version > current_version) {
+        && cmdstan_version_compare(latest_version, current_version) > 0) {
       packageStartupMessage(
         "\nA newer version of CmdStan is available. See ?install_cmdstan() to install it.",
         "\nTo disable this check set option or environment variable cmdstanr_no_ver_check=TRUE."
diff --git a/tests/testthat/test-install.R b/tests/testthat/test-install.R
index 243b803f..cfa21031 100644
--- a/tests/testthat/test-install.R
+++ b/tests/testthat/test-install.R
@@ -304,6 +304,20 @@ test_that("deprecated CMDSTANR_USE_MSYS_TOOLCHAIN is ignored with warning", {
   })
 })
 
+test_that("Rtools helpers compare R versions numerically", {
+  local({
+    local_mocked_bindings(current_r_version = function() numeric_version("4.10.0"))
+    expect_equal(rtools4x_version(), "45")
+  })
+  local({
+    local_mocked_bindings(
+      os_is_windows = function() TRUE,
+      current_r_version = function() numeric_version("4.10.0")
+    )
+    expect_equal(is_ucrt_toolchain(), TRUE)
+  })
+})
+
 test_that("rtools4x_toolchain_path prefers static-posix when available", {
   skip_if(arch_is_aarch64())
   env_var <- paste0(
diff --git a/tests/testthat/test-model-sample.R b/tests/testthat/test-model-sample.R
index 85c5dbb8..81186ed0 100644
--- a/tests/testthat/test-model-sample.R
+++ b/tests/testthat/test-model-sample.R
@@ -321,7 +321,7 @@ test_that("Correct behavior if fixed_param not set when the model has no paramet
   )
 
   reset_cmdstan_version(m)
-  if (cmdstan_version() >= "2.36.0") {
+  if (cmdstan_version_compare(cmdstan_version(), "2.36.0") >= 0) {
     # as of 2.36.0 we don't need fixed_param if no parameters
     expect_no_error(
       utils::capture.output(
diff --git a/tests/testthat/test-path.R b/tests/testthat/test-path.R
index 5b862a25..93f2d6c4 100644
--- a/tests/testthat/test-path.R
+++ b/tests/testthat/test-path.R
@@ -212,6 +212,18 @@ test_that("cmdstan_default_path() respects custom install directories", {
   )
 })
 
+test_that("cmdstan_default_path() orders install directories by CmdStan version", {
+  installs <- withr::local_tempdir(pattern = "cmdstan-version-installs")
+  dir.create(file.path(installs, "cmdstan-2.9.0"), recursive = TRUE, showWarnings = FALSE)
+  dir.create(file.path(installs, "cmdstan-2.35.0"), recursive = TRUE, showWarnings = FALSE)
+
+  expect_equal(latest_cmdstan_installed(installs), "cmdstan-2.35.0")
+  expect_equal(
+    cmdstan_default_path(dir = installs),
+    file.path(installs, "cmdstan-2.35.0")
+  )
+})
+
 test_that("cmdstan_default_path() returns NULL for empty custom install directories", {
   installs <- withr::local_tempdir(pattern = "cmdstan-empty-installs")
 
@@ -246,6 +258,13 @@ test_that("CmdStan version helpers handle invalid inputs", {
   expect_false(is_supported_cmdstan_version("not-a-version"))
 })
 
+test_that("CmdStan version helpers use numeric ordering", {
+  expect_equal(cmdstan_version_compare("cmdstan-2.35.0", "cmdstan-2.9.0"), 1)
+  expect_equal(cmdstan_version_compare("cmdstan-2.9.0", "cmdstan-2.35.0"), -1)
+  expect_equal(cmdstan_version_compare("2.36.0-rc1", "2.36.0"), 0)
+  expect_equal(cmdstan_version_compare("2.100.0", "2.36.0"), 1)
+})
+
 test_that("CmdStan version can be recovered from WSL UNC install path", {
   wsl_path <- "//wsl$/Ubuntu-22.04/root/.cmdstan/cmdstan-2.38.0"