diff --git a/src/SchemaSaurus.PostgreSql/PostgreSqlSchemaReader.Routines.cs b/src/SchemaSaurus.PostgreSql/PostgreSqlSchemaReader.Routines.cs
index a99a226..5fd459e 100644
--- a/src/SchemaSaurus.PostgreSql/PostgreSqlSchemaReader.Routines.cs
+++ b/src/SchemaSaurus.PostgreSql/PostgreSqlSchemaReader.Routines.cs
@@ -206,7 +206,6 @@ CROSS JOIN LATERAL unnest(
             WHERE {routineWhere}
                 AND ns.nspname NOT IN ('pg_catalog', 'information_schema'){schemaWhere}
                 AND NOT EXISTS (SELECT 1 FROM pg_depend dep WHERE dep.objid = proc.oid AND dep.deptype IN ('e', 'x'))
-                AND param.parameter_name IS NOT NULL
                 AND param.parameter_mode <> 't'
             ORDER BY proc.oid, param.ordinal_position
             """;
@@ -231,7 +230,12 @@ AND param.parameter_mode <> 't'
                 continue;
 
             var ordinal = (int)reader.GetInt64(positionOrdinal);
-            var parameterName = reader.GetString(nameOrdinal);
+            var parameterName = reader.GetStringNull(nameOrdinal);
+
+            // PostgreSQL leaves unnamed arguments as NULL or an empty string in proargnames; name them positionally
+            if (string.IsNullOrEmpty(parameterName))
+                parameterName = $"${ordinal}";
+
             var direction = MapParameterDirection(reader.GetString(directionOrdinal));
             var typeName = reader.GetString(typeNameOrdinal);
             var formattedTypeName = AdjustFormattedTypeName(reader.GetString(formattedTypeOrdinal));
diff --git a/test/SchemaSaurus.PostgreSql.Tests/Scripts/Script008.UnnamedParameters.sql b/test/SchemaSaurus.PostgreSql.Tests/Scripts/Script008.UnnamedParameters.sql
new file mode 100644
index 0000000..2e6973e
--- /dev/null
+++ b/test/SchemaSaurus.PostgreSql.Tests/Scripts/Script008.UnnamedParameters.sql
@@ -0,0 +1,29 @@
+-- unnamed input combined with a named OUT parameter => proargnames = {'', 'result'}
+CREATE OR REPLACE FUNCTION public."UnnamedInputWithOutput"(
+    integer,
+    OUT "Result" text
+)
+LANGUAGE sql
+AS $$
+    SELECT 'x'::text;
+$$;
+
+-- unnamed input on a RETURNS TABLE function => proargnames = {''}
+CREATE OR REPLACE FUNCTION public."UnnamedInputReturnsTable"(
+    integer
+)
+RETURNS TABLE ("Id" integer)
+LANGUAGE sql
+AS $$
+    SELECT 1;
+$$;
+
+-- no named parameters at all => proargnames IS NULL
+CREATE OR REPLACE FUNCTION public."UnnamedInputScalar"(
+    integer
+)
+RETURNS integer
+LANGUAGE sql
+AS $$
+    SELECT $1;
+$$;
diff --git a/test/SchemaSaurus.PostgreSql.Tests/UnnamedParameterTests.cs b/test/SchemaSaurus.PostgreSql.Tests/UnnamedParameterTests.cs
new file mode 100644
index 0000000..8ca8783
--- /dev/null
+++ b/test/SchemaSaurus.PostgreSql.Tests/UnnamedParameterTests.cs
@@ -0,0 +1,47 @@
+using SchemaSaurus.Metadata;
+using SchemaSaurus.PostgreSql.Tests.Fixtures;
+
+namespace SchemaSaurus.PostgreSql.Tests;
+
+public class UnnamedParameterTests(DatabaseFixture databaseFixture)
+    : SchemaReaderTestBase(databaseFixture)
+{
+    [Fact]
+    public async Task WhenFunctionHasUnnamedInputWithNamedOutputThenParametersArePositionallyNamed()
+    {
+        var model = await GetDatabaseModelAsync();
+        var func = model.ScalarFunctions.First(f => f.QualifiedName.Name == "UnnamedInputWithOutput");
+
+        func.Parameters.Should().HaveCount(2);
+
+        var input = func.Parameters.Single(p => p.Ordinal == 1);
+        input.Name.Should().Be("$1");
+        input.Direction.Should().Be(ParameterDirection.Input);
+        input.SystemType.Should().Be(typeof(int));
+
+        var output = func.Parameters.Single(p => p.Ordinal == 2);
+        output.Name.Should().Be("Result");
+        output.Direction.Should().Be(ParameterDirection.Output);
+    }
+
+    [Fact]
+    public async Task WhenTableValuedFunctionHasUnnamedInputThenParameterIsPositionallyNamed()
+    {
+        var model = await GetDatabaseModelAsync();
+        var func = model.TableValuedFunctions.First(f => f.QualifiedName.Name == "UnnamedInputReturnsTable");
+
+        func.Parameters.Should().HaveCount(1);
+        func.Parameters[0].Name.Should().Be("$1");
+        func.Parameters[0].Ordinal.Should().Be(1);
+    }
+
+    [Fact]
+    public async Task WhenFunctionHasNoNamedParametersThenParameterIsPositionallyNamed()
+    {
+        var model = await GetDatabaseModelAsync();
+        var func = model.ScalarFunctions.First(f => f.QualifiedName.Name == "UnnamedInputScalar");
+
+        func.Parameters.Should().HaveCount(1);
+        func.Parameters[0].Name.Should().Be("$1");
+    }
+}