diff --git a/DESCRIPTION b/DESCRIPTION
index 2e1613b7..68bb1bfc 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -17,6 +17,8 @@ Language: en-GB
 Config/testthat/edition: 3
 URL: https://github.com/mrc-ide/dust2
 BugReports: https://github.com/mrc-ide/dust2/issues
+Imports:
+    mcstate2
 LinkingTo:
     cpp11,
     mcstate2
diff --git a/inst/include/dust2/cpu.hpp b/inst/include/dust2/cpu.hpp
index 81f5a399..1f50d3f2 100644
--- a/inst/include/dust2/cpu.hpp
+++ b/inst/include/dust2/cpu.hpp
@@ -39,6 +39,7 @@ class dust_cpu {
     // Ignore errors for now.
     real_type * state_data = state_.data();
     real_type * state_next_data = state_next_.data();
+    // Later we parallelise this and track errors carefully.
     for (size_t i = 0; i < n_particles_; ++i) {
       const auto offset = i * n_state_;
       run_particle(time_, dt_, n_steps,
@@ -50,6 +51,12 @@ class dust_cpu {
     if (n_steps % 2 == 1) {
       std::swap(state_, state_next_);
     }
+    // Time management here is going to require some effort once we
+    // support interesting dt so that we always land on times with no
+    // non-integer bits, but for now we require that dt is 1 so this
+    // is easy.  We need this to hold within run_particle too, so it's
+    // possible that's where the calculation here will be done.
+    time_ = time_ + n_steps * dt_;
   }
 
   void set_state_initial() {
diff --git a/inst/include/dust2/r/cpu.hpp b/inst/include/dust2/r/cpu.hpp
index 857ff8c7..d5ba7a69 100644
--- a/inst/include/dust2/r/cpu.hpp
+++ b/inst/include/dust2/r/cpu.hpp
@@ -33,7 +33,12 @@ SEXP dust2_cpu_alloc(cpp11::list r_pars,
                              seed, deterministic);
   cpp11::external_pointer<dust_cpu<T>> ptr(obj, true, false);
 
-  return cpp11::writable::list({ptr});
+  // Later, we'll export a bit more back from the model (in particular
+  // models need to provide information about how they organise
+  // variables, ode models report computed control, etc.
+  auto size = T::size(shared);
+
+  return cpp11::writable::list{ptr, cpp11::as_sexp(size)};
 }
 
 template <typename T>
diff --git a/tests/testthat/test-walk.R b/tests/testthat/test-walk.R
index edb5a3c0..51042fc8 100644
--- a/tests/testthat/test-walk.R
+++ b/tests/testthat/test-walk.R
@@ -1,9 +1,20 @@
-test_that("...", {
+test_that("can run simple walk model", {
   pars <- list(sd = 1, random_initial = TRUE)
   obj <- dust2_cpu_walk_alloc(pars, 0, 1, 10, 42, FALSE)
+  expect_type(obj[[1]], "externalptr")
+  expect_equal(obj[[2]], 1)
+
   ptr <- obj[[1]]
-  dust2_cpu_walk_rng_state(ptr)
-  dust2_cpu_walk_state(ptr)
-  dust2_cpu_walk_run_steps(ptr, 3)
-  dust2_cpu_walk_state(ptr)
+  expect_type(dust2_cpu_walk_rng_state(ptr), "raw")
+  expect_length(dust2_cpu_walk_rng_state(ptr), 32 * 10)
+
+  expect_equal(dust2_cpu_walk_state(ptr), rep(0, 10))
+  expect_equal(dust2_cpu_walk_time(ptr), 0)
+
+  expect_null(dust2_cpu_walk_run_steps(ptr, 3))
+  s <- dust2_cpu_walk_state(ptr)
+
+  r <- mcstate2::mcstate_rng$new(seed = 42, n_streams = 10)
+  expect_equal(s, colSums(r$normal(3, 0, 1)))
+  expect_equal(dust2_cpu_walk_time(ptr), 3)
 })