diff --git a/src/test/test-models/good/services/zero_params.stan b/src/test/test-models/good/services/zero_params.stan
new file mode 100644
index 0000000000..46cb64ecfe
--- /dev/null
+++ b/src/test/test-models/good/services/zero_params.stan
@@ -0,0 +1,7 @@
+transformed data {
+  int N = 2;
+}
+generated quantities {
+  real theta = beta_rng(1, 1);
+  real eta = beta_rng(10, 10);
+}
diff --git a/src/test/unit/services/sample/hmc_nuts_dense_e_adapt_no_params_test.cpp b/src/test/unit/services/sample/hmc_nuts_dense_e_adapt_no_params_test.cpp
new file mode 100644
index 0000000000..a2e5781a60
--- /dev/null
+++ b/src/test/unit/services/sample/hmc_nuts_dense_e_adapt_no_params_test.cpp
@@ -0,0 +1,177 @@
+#include <stan/services/sample/hmc_nuts_dense_e.hpp>
+#include <gtest/gtest.h>
+#include <stan/io/empty_var_context.hpp>
+#include <test/test-models/good/services/zero_params.hpp>
+#include <test/unit/services/instrumented_callbacks.hpp>
+#include <iostream>
+
+auto&& blah = stan::math::init_threadpool_tbb();
+
+static constexpr size_t num_chains = 4;
+class ServicesSampleHMCNutsDenseENoParams : public testing::Test {
+ public:
+  ServicesSampleHMCNutsDenseENoParams() : model(data_context, 0, &model_log) {
+    for (int i = 0; i < num_chains; ++i) {
+      init.push_back(stan::test::unit::instrumented_writer{});
+      parameter.push_back(stan::test::unit::instrumented_writer{});
+      diagnostic.push_back(stan::test::unit::instrumented_writer{});
+      context.push_back(std::make_shared<stan::io::empty_var_context>());
+    }
+  }
+  stan::io::empty_var_context data_context;
+  std::stringstream model_log;
+  stan::test::unit::instrumented_logger logger;
+  std::vector<stan::test::unit::instrumented_writer> init;
+  std::vector<stan::test::unit::instrumented_writer> parameter;
+  std::vector<stan::test::unit::instrumented_writer> diagnostic;
+  std::vector<std::shared_ptr<stan::io::empty_var_context>> context;
+  stan_model model;
+};
+
+TEST_F(ServicesSampleHMCNutsDenseENoParams, call_count) {
+  unsigned int random_seed = 0;
+  unsigned int chain = 1;
+  double init_radius = 0;
+  int num_warmup = 200;
+  int num_samples = 400;
+  int num_thin = 5;
+  bool save_warmup = true;
+  int refresh = 0;
+  double stepsize = 0.1;
+  double stepsize_jitter = 0;
+  int max_depth = 8;
+  double delta = .1;
+  double gamma = .1;
+  double kappa = .1;
+  double t0 = .1;
+  unsigned int init_buffer = 50;
+  unsigned int term_buffer = 50;
+  unsigned int window = 100;
+  stan::test::unit::instrumented_interrupt interrupt;
+  EXPECT_EQ(interrupt.call_count(), 0);
+
+  int return_code = stan::services::sample::hmc_nuts_dense_e(
+      model, num_chains, context, random_seed, chain, init_radius, num_warmup,
+      num_samples, num_thin, save_warmup, refresh, stepsize, stepsize_jitter,
+      max_depth, interrupt, logger, init, parameter, diagnostic);
+
+  EXPECT_EQ(0, return_code);
+
+  int num_output_lines = (num_warmup + num_samples) / num_thin;
+  EXPECT_EQ((num_warmup + num_samples) * num_chains, interrupt.call_count());
+  for (int i = 0; i < num_chains; ++i) {
+    EXPECT_EQ(1, parameter[i].call_count("vector_string"));
+    EXPECT_EQ(num_output_lines, parameter[i].call_count("vector_double"));
+    EXPECT_EQ(1, diagnostic[i].call_count("vector_string"));
+    EXPECT_EQ(num_output_lines, diagnostic[i].call_count("vector_double"));
+  }
+}
+
+TEST_F(ServicesSampleHMCNutsDenseENoParams, parameter_checks) {
+  unsigned int random_seed = 0;
+  unsigned int chain = 1;
+  double init_radius = 0;
+  int num_warmup = 200;
+  int num_samples = 400;
+  int num_thin = 5;
+  bool save_warmup = true;
+  int refresh = 0;
+  double stepsize = 0.1;
+  double stepsize_jitter = 0;
+  int max_depth = 8;
+  double delta = .1;
+  double gamma = .1;
+  double kappa = .1;
+  double t0 = .1;
+  unsigned int init_buffer = 50;
+  unsigned int term_buffer = 50;
+  unsigned int window = 100;
+  stan::test::unit::instrumented_interrupt interrupt;
+  EXPECT_EQ(interrupt.call_count(), 0);
+
+  int return_code = stan::services::sample::hmc_nuts_dense_e(
+      model, num_chains, context, random_seed, chain, init_radius, num_warmup,
+      num_samples, num_thin, save_warmup, refresh, stepsize, stepsize_jitter,
+      max_depth, interrupt, logger, init, parameter, diagnostic);
+
+  for (size_t i = 0; i < num_chains; ++i) {
+    std::vector<std::vector<std::string>> parameter_names;
+    parameter_names = parameter[i].vector_string_values();
+    std::vector<std::vector<double>> parameter_values;
+    parameter_values = parameter[i].vector_double_values();
+    std::vector<std::string> strings;
+    strings = parameter[i].string_values();
+    std::vector<std::vector<std::string>> diagnostic_names;
+    diagnostic_names = diagnostic[i].vector_string_values();
+    std::vector<std::vector<double>> diagnostic_values;
+    diagnostic_values = diagnostic[i].vector_double_values();
+
+    // Expect message at end of warmup
+    EXPECT_EQ("Adaptation terminated", strings[0]);
+
+    // Expectations of sampler and model variables names.
+    ASSERT_EQ(9, parameter_names[0].size());
+    EXPECT_EQ("lp__", parameter_names[0][0]);
+    EXPECT_EQ("accept_stat__", parameter_names[0][1]);
+    EXPECT_EQ("stepsize__", parameter_names[0][2]);
+    EXPECT_EQ("treedepth__", parameter_names[0][3]);
+    EXPECT_EQ("n_leapfrog__", parameter_names[0][4]);
+    EXPECT_EQ("divergent__", parameter_names[0][5]);
+    EXPECT_EQ("energy__", parameter_names[0][6]);
+    EXPECT_EQ("theta", parameter_names[0][7]);
+    EXPECT_EQ("eta", parameter_names[0][8]);
+
+    // Expect one name per parameter value.
+    EXPECT_EQ(parameter_names[0].size(), parameter_values[0].size());
+    EXPECT_EQ(diagnostic_names[0].size(), diagnostic_values[0].size());
+
+    EXPECT_EQ((num_warmup + num_samples) / num_thin, parameter_values.size());
+
+    // Expect one call to set parameter names, and one set of output per
+    // iteration.
+    EXPECT_EQ("lp__", diagnostic_names[0][0]);
+    EXPECT_EQ("accept_stat__", diagnostic_names[0][1]);
+  }
+  EXPECT_EQ(return_code, 0);
+}
+
+TEST_F(ServicesSampleHMCNutsDenseENoParams, output_regression) {
+  unsigned int random_seed = 0;
+  unsigned int chain = 1;
+  double init_radius = 0;
+  int num_warmup = 200;
+  int num_samples = 400;
+  int num_thin = 5;
+  bool save_warmup = true;
+  int refresh = 0;
+  double stepsize = 0.1;
+  double stepsize_jitter = 0;
+  int max_depth = 8;
+  double delta = .1;
+  double gamma = .1;
+  double kappa = .1;
+  double t0 = .1;
+  unsigned int init_buffer = 50;
+  unsigned int term_buffer = 50;
+  unsigned int window = 100;
+  stan::test::unit::instrumented_interrupt interrupt;
+  EXPECT_EQ(interrupt.call_count(), 0);
+
+  stan::services::sample::hmc_nuts_dense_e(
+      model, num_chains, context, random_seed, chain, init_radius, num_warmup,
+      num_samples, num_thin, save_warmup, refresh, stepsize, stepsize_jitter,
+      max_depth, interrupt, logger, init, parameter, diagnostic);
+
+  for (auto&& init_it : init) {
+    std::vector<std::string> init_values;
+    init_values = init_it.string_values();
+
+    EXPECT_EQ(0, init_values.size());
+  }
+
+  EXPECT_EQ(num_chains, logger.find_info("Elapsed Time:"));
+  EXPECT_EQ(num_chains, logger.find_info("seconds (Warm-up)"));
+  EXPECT_EQ(num_chains, logger.find_info("seconds (Sampling)"));
+  EXPECT_EQ(num_chains, logger.find_info("seconds (Total)"));
+  EXPECT_EQ(0, logger.call_count_error());
+}
diff --git a/src/test/unit/services/util/inv_metric_test.cpp b/src/test/unit/services/util/inv_metric_test.cpp
index eb6bb0459b..92892a6405 100644
--- a/src/test/unit/services/util/inv_metric_test.cpp
+++ b/src/test/unit/services/util/inv_metric_test.cpp
@@ -27,6 +27,13 @@ TEST(inv_metric, create_diag_sz100) {
   ASSERT_NEAR(1.0, diag_vals[99], 0.0001);
 }
 
+TEST(inv_metric, create_dense_sz0) {
+  auto default_metric = stan::services::util::create_unit_e_dense_inv_metric(0);
+  stan::io::var_context& inv_inv_metric = default_metric;
+  std::vector<double> diag_vals = inv_inv_metric.vals_r("inv_metric");
+  EXPECT_EQ(0, diag_vals.size());
+}
+
 TEST(inv_metric, create_dense_sz2) {
   auto default_metric = stan::services::util::create_unit_e_dense_inv_metric(2);
   stan::io::var_context& inv_inv_metric = default_metric;
@@ -122,9 +129,9 @@ TEST(inv_metric, read_dense_OK) {
 
 TEST(inv_metric, read_dense_sz0) {
   stan::callbacks::logger logger;
-  stan::io::dump dmp = stan::services::util::create_unit_e_dense_inv_metric(0);
+  auto zero_metric = stan::services::util::create_unit_e_dense_inv_metric(0);
   Eigen::MatrixXd inv_inv_metric
-      = stan::services::util::read_dense_inv_metric(dmp, 0, logger);
+      = stan::services::util::read_dense_inv_metric(zero_metric, 0, logger);
   EXPECT_EQ(0, inv_inv_metric.size());
   EXPECT_EQ(0, inv_inv_metric.rows());
   EXPECT_EQ(0, inv_inv_metric.cols());