diff --git a/src/anthem/Translation.cpp b/src/anthem/Translation.cpp
index 9601a83..f819e37 100644
--- a/src/anthem/Translation.cpp
+++ b/src/anthem/Translation.cpp
@@ -58,14 +58,15 @@ void translate(const char *fileName, std::istream &stream, Context &context)
 
 	Clingo::parse_program(fileContent.c_str(), translateStatement, logger);
 
-	if (context.performSimplification)
-		for (auto &scopedFormula : scopedFormulas)
-			simplify(scopedFormula.formula);
-
 	ast::PrintContext printContext(context);
 
 	if (!context.performCompletion)
 	{
+		// Simplify output if specified
+		if (context.performSimplification)
+			for (auto &scopedFormula : scopedFormulas)
+				simplify(scopedFormula.formula);
+
 		if (context.visiblePredicateSignatures)
 			context.logger.log(output::Priority::Warning) << "#show statements are ignored because completion is not enabled";
 
@@ -78,9 +79,10 @@ void translate(const char *fileName, std::istream &stream, Context &context)
 		return;
 	}
 
+	// Perform completion
 	auto completedFormulas = complete(std::move(scopedFormulas), context);
 
-	// TODO: rethink simplification steps
+	// Simplify output if specified
 	if (context.performSimplification)
 		for (auto &completedFormula : completedFormulas)
 			simplify(completedFormula);
diff --git a/tests/TestHiddenPredicateElimination.cpp b/tests/TestHiddenPredicateElimination.cpp
index b1b17ed..fa7a6b5 100644
--- a/tests/TestHiddenPredicateElimination.cpp
+++ b/tests/TestHiddenPredicateElimination.cpp
@@ -137,4 +137,18 @@ TEST_CASE("[hidden predicate elimination] Hidden predicates are correctly elimin
 		CHECK(output.str() ==
 			"forall V1, V2 (a(V1, V2) <-> exists U1 ((V1 = 1 and V2 = 2 and U1 = 3) or (V1 = 2 and V2 = 4 and U1 = 6)))\n");
 	}
+
+	SECTION("nested arguments are correctly handled when hiding predicates")
+	{
+		input <<
+			"a(X) :- b(c(X)).\n"
+			"b(c(X)) :- c(X).\n"
+			"c(1..4).\n"
+			"#show a/1.";
+		anthem::translate("input", input, context);
+
+		// TODO: simplify further
+		CHECK(output.str() ==
+			"forall V1 (a(V1) <-> exists U1 (c(V1) = c(U1) and U1 in 1..4))\n");
+	}
 }