diff --git a/test/ExecutionFramework.h b/test/ExecutionFramework.h
index b20f10f9c..5019c0fbc 100644
--- a/test/ExecutionFramework.h
+++ b/test/ExecutionFramework.h
@@ -92,6 +92,12 @@ public:
 		return callFallbackWithValue(0);
 	}
 
+	bytes const& callLowLevel(bytes const& _data, u256 const& _value)
+	{
+		sendMessage(_data, false, _value);
+		return m_output;
+	}
+
 	bytes const& callContractFunctionWithValueNoEncoding(std::string _sig, u256 const& _value, bytes const& _arguments)
 	{
 		FixedHash<4> hash(dev::keccak256(_sig));
diff --git a/test/libsolidity/SemanticTest.cpp b/test/libsolidity/SemanticTest.cpp
index dd95c4dee..cdb4e3625 100644
--- a/test/libsolidity/SemanticTest.cpp
+++ b/test/libsolidity/SemanticTest.cpp
@@ -98,11 +98,13 @@ TestCase::TestResult SemanticTest::run(ostream& _stream, string const& _linePref
 			}
 			else
 			{
-				bytes output = callContractFunctionWithValueNoEncoding(
-					test.call().signature,
-					test.call().value,
-					test.call().arguments.rawBytes()
-				);
+				bytes output = test.call().useCallWithoutSignature ?
+					callLowLevel(test.call().arguments.rawBytes(), test.call().value) :
+					callContractFunctionWithValueNoEncoding(
+						test.call().signature,
+						test.call().value,
+						test.call().arguments.rawBytes()
+					);
 
 				if ((m_transactionSuccessful == test.call().expectations.failure) || (output != test.call().expectations.rawBytes()))
 					success = false;
diff --git a/test/libsolidity/SolidityEndToEndTest.cpp b/test/libsolidity/SolidityEndToEndTest.cpp
index 903740182..af940e0ef 100644
--- a/test/libsolidity/SolidityEndToEndTest.cpp
+++ b/test/libsolidity/SolidityEndToEndTest.cpp
@@ -2514,23 +2514,6 @@ BOOST_AUTO_TEST_CASE(super_alone)
 	)
 }
 
-BOOST_AUTO_TEST_CASE(fallback_function)
-{
-	char const* sourceCode = R"(
-		contract A {
-			uint data;
-			function() external { data = 1; }
-			function getData() public returns (uint r) { return data; }
-		}
-	)";
-	ALSO_VIA_YUL(
-		compileAndRun(sourceCode);
-		ABI_CHECK(callContractFunction("getData()"), encodeArgs(0));
-		ABI_CHECK(callContractFunction(""), encodeArgs());
-		ABI_CHECK(callContractFunction("getData()"), encodeArgs(1));
-	)
-}
-
 BOOST_AUTO_TEST_CASE(inherited_fallback_function)
 {
 	char const* sourceCode = R"(
diff --git a/test/libsolidity/semanticTests/smoke/fallback.sol b/test/libsolidity/semanticTests/smoke/fallback.sol
new file mode 100644
index 000000000..71d17cf0c
--- /dev/null
+++ b/test/libsolidity/semanticTests/smoke/fallback.sol
@@ -0,0 +1,23 @@
+contract A {
+    uint public data;
+    uint public balance;
+    bytes public externalData;
+    function() external payable {
+        data += 1;
+        balance = msg.value;
+        externalData = msg.data;
+    }
+}
+// ----
+// data() -> 0
+// ()
+// data() -> 1
+// (): hex"42ef"
+// data() -> 2
+// externalData() -> 0x20, 2, left(0x42ef)
+// balance() -> 0
+// (), 1 ether
+// balance() -> 1
+// (), 2 ether: hex"fefe"
+// balance() -> 2
+// externalData() -> 0x20, 2, left(0xfefe)
\ No newline at end of file
diff --git a/test/libsolidity/util/SoltestTypes.h b/test/libsolidity/util/SoltestTypes.h
index 0e7a3072c..275b1e657 100644
--- a/test/libsolidity/util/SoltestTypes.h
+++ b/test/libsolidity/util/SoltestTypes.h
@@ -262,6 +262,9 @@ struct FunctionCall
 	DisplayMode displayMode = DisplayMode::SingleLine;
 	/// Marks this function call as the constructor.
 	bool isConstructor = false;
+	/// If this function call's signature has no name and no arguments,
+	/// a low-level call with unstructured calldata will be issued.
+	bool useCallWithoutSignature = false;
 	/// Marks this function call as "short-handed", meaning
 	/// no `->` declared.
 	bool omitsArrow = true;
diff --git a/test/libsolidity/util/TestFileParser.cpp b/test/libsolidity/util/TestFileParser.cpp
index ebb865b4f..f33853dfe 100644
--- a/test/libsolidity/util/TestFileParser.cpp
+++ b/test/libsolidity/util/TestFileParser.cpp
@@ -75,7 +75,7 @@ vector<dev::solidity::test::FunctionCall> TestFileParser::parseFunctionCalls(siz
 
 				try
 				{
-					call.signature = parseFunctionSignature();
+					tie(call.signature, call.useCallWithoutSignature) = parseFunctionSignature();
 					if (accept(Token::Comma, true))
 						call.value = parseFunctionCallValue();
 					if (accept(Token::Colon, true))
@@ -148,10 +148,17 @@ bool TestFileParser::expect(soltest::Token _token, bool const _advance)
 	return true;
 }
 
-string TestFileParser::parseFunctionSignature()
+pair<string, bool> TestFileParser::parseFunctionSignature()
 {
-	string signature = m_scanner.currentLiteral();
-	expect(Token::Identifier);
+	string signature;
+	bool hasName = false;
+
+	if (accept(Token::Identifier, false))
+	{
+		hasName = true;
+		signature = m_scanner.currentLiteral();
+		expect(Token::Identifier);
+	}
 
 	signature += formatToken(Token::LParen);
 	expect(Token::LParen);
@@ -169,11 +176,15 @@ string TestFileParser::parseFunctionSignature()
 	if (accept(Token::Arrow, true))
 		throw Error(Error::Type::ParserError, "Invalid signature detected: " + signature);
 
-	signature += parameters;
+	if (!hasName && !parameters.empty())
+		throw Error(Error::Type::ParserError, "Signatures without a name cannot have parameters: " + signature);
+	else
+		signature += parameters;
 
 	expect(Token::RParen);
 	signature += formatToken(Token::RParen);
-	return signature;
+
+	return {signature, !hasName};
 }
 
 u256 TestFileParser::parseFunctionCallValue()
diff --git a/test/libsolidity/util/TestFileParser.h b/test/libsolidity/util/TestFileParser.h
index dc3775357..a460f4d40 100644
--- a/test/libsolidity/util/TestFileParser.h
+++ b/test/libsolidity/util/TestFileParser.h
@@ -46,6 +46,8 @@ namespace test
  * // -> 2, 3
  * // h(uint256), 1 ether: 42
  * // -> FAILURE                # If REVERT or other EVM failure was detected #
+ * // ()                        # Call fallback function #
+ * // (), 1 ether               # Call ether function #
  * ...
  */
 class TestFileParser
@@ -128,8 +130,10 @@ private:
 	bool accept(soltest::Token _token, bool const _expect = false);
 	bool expect(soltest::Token _token, bool const _advance = true);
 
-	/// Parses a function call signature in the form of f(uint256, ...).
-	std::string parseFunctionSignature();
+	/// Parses a function call signature in the form of `f(uint256, ...)` and
+	/// returns the signature and a flag that indicates if the function name was
+	/// empty. If so, the signature is not allowed to define any parameters.
+	std::pair<std::string, bool> parseFunctionSignature();
 
 	/// Parses the optional ether value that can be passed alongside the
 	/// function call arguments. Throws an InvalidEtherValueEncoding exception