diff --git a/README.md b/README.md
index 521b8b1..ac5fe07 100644
--- a/README.md
+++ b/README.md
@@ -238,7 +238,18 @@ steps:
 ```
 
 The test requires [`criterion`](https://github.com/bheisler/criterion.rs)
-benchmarks to be exported by the crate. `criterion` collects performance
+benchmarks to be exported by the crate. The test expects the entry point
+into the performance benchmarks to be named `main`. In other words, the
+following configuration is expected in `Cargo.toml`:
+```toml
+[[bench]]
+name = "main"
+```
+
+All benchmarks need to be collected in a main.rs file placed in `benches/`.
+
+
+`criterion` collects performance
 results by running a function for a user-configured number of iterations,
 timing the runs, and applying statistics. The individual benchmark tests must
 be added in the crate. They can be run outside the CI with:
diff --git a/integration_tests/test_benchmark.py b/integration_tests/test_benchmark.py
index 41e432a..5c18631 100644
--- a/integration_tests/test_benchmark.py
+++ b/integration_tests/test_benchmark.py
@@ -18,7 +18,10 @@ def test_bench():
     os.chdir(get_repo_root_path())
 
     # Get numbers for current HEAD.
-    _run_cargo_bench("after")
+    return_code, stdout, stderr = _run_cargo_bench("after")
+    # Even if it is the first time this test is run, the benchmark tests should pass.
+    # For this purpose, we need to explicitly check the return code.
+    assert return_code == 0, "stdout: {}\n stderr: {}".format(stdout, stderr)
 
     # Move to upstream tip.
     subprocess.run(
@@ -31,9 +34,33 @@ def test_bench():
     )
 
     # Get numbers from upstream tip, without the changes from the current PR.
-    _run_cargo_bench("before")
+    return_code, stdout, stderr = _run_cargo_bench("before")
+    if return_code == 0:
+        # In case this benchmark also ran successfully, we can call critcmp and compare the results.
+        _run_critcmp()
+    else:
+        # The benchmark did not run successfully, but it might be that it is because a benchmark does not exist.
+        # In this case, we do not want to fail the test.
+        if "error: no bench target named `main`" in stderr:
+            # This is a bit of a &*%^ way of checking if the benchmark does not exist.
+            # Hopefully it will be possible to check it in another way...soon
+            print("There are no benchmarks in master. No comparison can happen.")
+        else:
+            assert return_code == 0, "stdout: {}\n stderr: {}".format(stdout, stderr)
 
-    # Compare.
+
+def _run_cargo_bench(baseline):
+    """Runs `cargo bench` and tags the baseline."""
+    process = subprocess.run(
+        "cargo bench --bench main --all-features -- --noplot --save-baseline {}"
+        .format(baseline),
+        shell=True, stderr=subprocess.PIPE, stdout=subprocess.PIPE
+    )
+
+    return process.returncode, process.stdout.decode('utf-8'), process.stderr.decode('utf-8')
+
+
+def _run_critcmp():
     p = subprocess.run(
         "critcmp before after",
         shell=True, check=True,
@@ -44,12 +71,3 @@ def test_bench():
     print(p.stdout.decode('utf-8'))
     print('ERRORS')
     print(p.stderr.decode('utf-8'))
-
-
-def _run_cargo_bench(baseline):
-    """Runs `cargo bench` and tags the baseline."""
-    subprocess.run(
-        "cargo bench --all-features -- --noplot --save-baseline {}"
-        .format(baseline),
-        shell=True, check=True
-    )