diff --git a/CHANGELOG.md b/CHANGELOG.md
index 39cd61e..3041b5c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -16,7 +16,8 @@
 
 ## Changes
 
-- When parameters are used with `--parameter-list` or `--parameter-scan`, the JSON export format now contains a dictionary `parameters` instead of a single key `parameter`.
+- When parameters are used with `--parameter-list` or `--parameter-scan`, the JSON export format now contains a dictionary `parameters` instead of a single key `parameter`. See #253, #318.
+- The `plot_parametrized.py` script now infers the parameter name, and its `--parameter-name` argument has been deprecated. See #253, #318.
 
 ## Bugfixes
 ## Other
diff --git a/scripts/plot_parametrized.py b/scripts/plot_parametrized.py
index fbe9205..48f354c 100755
--- a/scripts/plot_parametrized.py
+++ b/scripts/plot_parametrized.py
@@ -6,6 +6,7 @@ errorbar plot."""
 import argparse
 import json
 import matplotlib.pyplot as plt
+import sys
 
 parser = argparse.ArgumentParser(description=__doc__)
 parser.add_argument("file", help="JSON file with benchmark results", nargs="+")
@@ -13,7 +14,7 @@ parser.add_argument(
     "--parameter-name",
     metavar="name",
     type=str,
-    help="Name of the parameter / x-axis label",
+    help="Deprecated; parameter names are now inferred from benchmark files",
 )
 parser.add_argument(
     "--log-x", help="Use a logarithmic x (parameter) axis", action="store_true"
@@ -26,18 +27,66 @@ parser.add_argument(
 )
 
 args = parser.parse_args()
+if args.parameter_name is not None:
+    sys.stderr.write(
+        "warning: --parameter-name is deprecated; names are inferred from "
+        "benchmark results\n"
+    )
+
+
+def die(msg):
+    sys.stderr.write("fatal: %s\n" % (msg,))
+    sys.exit(1)
+
+
+def extract_parameters(results):
+    """Return `(parameter_name: str, parameter_values: List[float])`."""
+    if not results:
+        die("no benchmark data to plot")
+    (names, values) = zip(*(unique_parameter(b) for b in results))
+    names = frozenset(names)
+    if len(names) != 1:
+        die(
+            "benchmarks must all have the same parameter name, but found: %s"
+            % sorted(names)
+        )
+    return (next(iter(names)), values)
+
+
+def unique_parameter(benchmark):
+    """Return the unique parameter `(name: str, value: float)`, or dies."""
+    params_dict = benchmark.get("parameters", {})
+    if not params_dict:
+        die("benchmarks must have exactly one parameter, but found none")
+    if len(params_dict) > 1:
+        die(
+            "benchmarks must have exactly one parameter, but found multiple: %s"
+            % sorted(params_dict)
+        )
+    return next(iter(params_dict.items()))
+
+
+parameter_name = None
 
 for filename in args.file:
     with open(filename) as f:
         results = json.load(f)["results"]
 
-    parameter_values = [float(b["parameter"]) for b in results]
+    (this_parameter_name, parameter_values) = extract_parameters(results)
+    if parameter_name is not None and this_parameter_name != parameter_name:
+        die(
+            "files must all have the same parameter name, but found %r vs. %r"
+            % (parameter_name, this_parameter_name)
+        )
+    parameter_name = this_parameter_name
+
+    parameter_values = [float(pv) for pv in parameter_values]
     times_mean = [b["mean"] for b in results]
     times_stddev = [b["stddev"] for b in results]
 
     plt.errorbar(x=parameter_values, y=times_mean, yerr=times_stddev, capsize=2)
 
-plt.xlabel(args.parameter_name)
+plt.xlabel(parameter_name)
 plt.ylabel("Time [s]")
 
 if args.log_time: