diff --git a/R/mortality_processes.R b/R/mortality_processes.R
index 976383c0..5884c928 100644
--- a/R/mortality_processes.R
+++ b/R/mortality_processes.R
@@ -19,7 +19,7 @@ create_mortality_process <- function(variables, events, renderer, parameters) {
       renderer$render('natural_deaths', died$size(), timestep)
     } else {
       age <- get_age(variables$birth$get_values(), timestep)
-      last_deathrate <- match_last_timestep(parameters$deathrate_timesteps, timestep)
+      last_deathrate <- match_timestep(parameters$deathrate_timesteps, timestep)
       deathrates <- rep(1, pop)
       age_groups <- .bincode(age, c(0, parameters$deathrate_agegroups))
       in_range <- !is.na(age_groups)
diff --git a/R/population_parameters.R b/R/population_parameters.R
index 3b08cc3d..89015790 100644
--- a/R/population_parameters.R
+++ b/R/population_parameters.R
@@ -73,6 +73,6 @@ find_birthrates <- function(pops, age_high, deathrates) {
 }
 
 get_human_population <- function(parameters, timestep) {
-  last_pop <- match_last_timestep(parameters$human_population_timesteps, timestep)
+  last_pop <- match_timestep(parameters$human_population_timesteps, timestep)
   parameters$human_population[last_pop]
 }
diff --git a/R/utils.R b/R/utils.R
index f2b3dfd1..343e6309 100644
--- a/R/utils.R
+++ b/R/utils.R
@@ -62,14 +62,6 @@ rtexp <- function(n, m, t) { itexp(runif(n), m, t) }
 #'@param t current timestep
 #'@noRd
 match_timestep <- function(ts, t) {
-  min(sum(ts < t) + 1, length(ts))
-}
-
-#'@title Find index of the latest timestep in vector of timesteps
-#'@param ts timesteps, assumed to be sorted and unique
-#'@param t current timestep
-#'@noRd
-match_last_timestep <- function(ts, t) {
   min(sum(ts <= t), length(ts))
 }
 
diff --git a/tests/testthat/test-demography.R b/tests/testthat/test-demography.R
index c471fe90..572706c2 100644
--- a/tests/testthat/test-demography.R
+++ b/tests/testthat/test-demography.R
@@ -55,3 +55,19 @@ test_that('calculate_initial_ages calculates truncated exp custom demographic',
   mockery::expect_args(mock_rtexp, 2, 2, .75, 50 * 365)
   expect_setequal(ages, c(25 * 365, 75 * 365, 30 * 365, 80 * 365))
 })
+
+test_that('match_timestep always gives 0 for constant demography', {
+  expect_equal(match_timestep(c(0), 0), 1)
+  expect_equal(match_timestep(c(0), 1), 1)
+  expect_equal(match_timestep(c(0), 50), 1)
+})
+
+test_that('match_timestep works on the boundaries', {
+  expect_equal(match_timestep(c(0, 50, 100), 0), 1)
+  expect_equal(match_timestep(c(0, 50, 100), 1), 1)
+  expect_equal(match_timestep(c(0, 50, 100), 49), 1)
+  expect_equal(match_timestep(c(0, 50, 100), 50), 2)
+  expect_equal(match_timestep(c(0, 50, 100), 99), 2)
+  expect_equal(match_timestep(c(0, 50, 100), 100), 3)
+  expect_equal(match_timestep(c(0, 50, 100), 101), 3)
+})
\ No newline at end of file