diff --git a/tests/testthat/setup.R b/tests/testthat/setup.R
index 89236eacf..fdb43875b 100644
--- a/tests/testthat/setup.R
+++ b/tests/testthat/setup.R
@@ -388,4 +388,12 @@ ziplss_data <- function(seed = 0) {
 ziplss_df <- ziplss_data()
 m_ziplss <- gam(list(y ~ s(x2) + x3,
   ~ s(x0) + x1), family = ziplss(), data = ziplss_df)
-    
\ No newline at end of file
+
+# TWLSS example from ?mgcv::twlss
+twlss_df <- withr::with_seed(3, gamSim(1, n = 400, dist = "poisson",
+    scale = 0.2, verbose = FALSE) |>
+  mutate(y = mgcv::rTweedie(exp(.data$f), p = 1.3,
+    phi = 0.5))) ## Tweedie response
+## Fit a fixed p Tweedie, with wrong link ...
+m_twlss <- gam(list(y ~ s(x0) + s(x1) + s(x2) + s(x3), ~ 1, ~ 1),
+  family = twlss(), data = twlss_df)
diff --git a/tests/testthat/test-fitted-values.R b/tests/testthat/test-fitted-values.R
index 3fb413761..f81c1281d 100644
--- a/tests/testthat/test-fitted-values.R
+++ b/tests/testthat/test-fitted-values.R
@@ -89,6 +89,13 @@ test_that("fitted values works for a gaulss model", {
     expect_named(fv, expected = c(".row", ".parameter", fv_nms))
 })
 
+test_that("fitted values works for a twlss model", {
+    expect_silent(fv <- fitted_values(m_twlss))
+    expect_named(fv, expected = c(".row", ".parameter", fv_nms))
+    expect_identical(pull(fv, ".parameter") |> unique(),
+        c("location", "power", "scale"))
+})
+
 test_that("fitted values works for a gamm model", {
     expect_silent(fv <- fitted_values(m_gamm))
     expect_named(fv, expected = c(".row","x0", "x1", "x2", "x3", fv_nms))