diff --git a/R/pareto_smooth.R b/R/pareto_smooth.R
index 7de50fa9..b82accec 100644
--- a/R/pareto_smooth.R
+++ b/R/pareto_smooth.R
@@ -345,7 +345,11 @@ pareto_smooth.default <- function(x,
     )
     right_k <- smoothed$k
 
-    k <- max(left_k, right_k, na.rm = TRUE)
+    if (is.na(left_k) && is.na(right_k)) {
+      k <- NA
+    } else {
+      k <- max(left_k, right_k, na.rm = TRUE)
+    }
     x <- smoothed$x
 
   } else {
diff --git a/tests/testthat/test-pareto_smooth.R b/tests/testthat/test-pareto_smooth.R
index b4203097..d9dc10d1 100644
--- a/tests/testthat/test-pareto_smooth.R
+++ b/tests/testthat/test-pareto_smooth.R
@@ -13,6 +13,18 @@ test_that("pareto_khat handles constant tail correctly", {
 })
 
 
+test_that("pareto_khat handles both tails being constant correctly", {
+
+  # left and right tails are constant, so khat should be NA in all cases
+  x <- c(rep(-100, 10), sort(rnorm(100)), rep(100, 10))
+  
+  expect_true(is.na(pareto_khat(x, tail = "left", ndraws_tail = 10)))
+  expect_true(is.na(pareto_khat(x, tail = "right", ndraws_tail = 10)))
+  expect_true(is.na(pareto_khat(x, tail = "both", ndraws_tail = 10)))
+
+})
+
+
 test_that("pareto_smooth handles non-constant x with constant tail", {
 
   # x is non-constant but the right tail is constant
@@ -281,4 +293,4 @@ test_that("check ps_min_ss behavior special cases", {
   expect_true(is.infinite(ps_min_ss(2)))
   # k < 1
   expect_equal(ps_min_ss(0.5), 10^(1 / (1 - max(0, 0.5))))
-})
\ No newline at end of file
+})