diff --git a/libsolidity/SolidityOptimizer.cpp b/libsolidity/SolidityOptimizer.cpp
index 9cdaa5886..3cb6a536a 100644
--- a/libsolidity/SolidityOptimizer.cpp
+++ b/libsolidity/SolidityOptimizer.cpp
@@ -83,14 +83,28 @@ public:
 							"\nOptimized:     " + toHex(optimizedOutput));
 	}
 
-	AssemblyItems getCSE(AssemblyItems const& _input)
+	AssemblyItems addDummyLocations(AssemblyItems const& _input)
 	{
 		// add dummy locations to each item so that we can check that they are not deleted
 		AssemblyItems input = _input;
 		for (AssemblyItem& item: input)
 			item.setLocation(SourceLocation(1, 3, make_shared<string>("")));
+		return input;
+	}
 
-		eth::CommonSubexpressionEliminator cse;
+	eth::KnownState createInitialState(AssemblyItems const& _input)
+	{
+		eth::KnownState state;
+		for (auto const& item: addDummyLocations(_input))
+			state.feedItem(item);
+		return state;
+	}
+
+	AssemblyItems getCSE(AssemblyItems const& _input, eth::KnownState const& _state = eth::KnownState())
+	{
+		AssemblyItems input = addDummyLocations(_input);
+
+		eth::CommonSubexpressionEliminator cse(_state);
 		BOOST_REQUIRE(cse.feedItems(input.begin(), input.end()) == input.end());
 		AssemblyItems output = cse.getOptimizedItems();
 
@@ -101,9 +115,13 @@ public:
 		return output;
 	}
 
-	void checkCSE(AssemblyItems const& _input, AssemblyItems const& _expectation)
+	void checkCSE(
+		AssemblyItems const& _input,
+		AssemblyItems const& _expectation,
+		KnownState const& _state = eth::KnownState()
+	)
 	{
-		AssemblyItems output = getCSE(_input);
+		AssemblyItems output = getCSE(_input, _state);
 		BOOST_CHECK_EQUAL_COLLECTIONS(_expectation.begin(), _expectation.end(), output.begin(), output.end());
 	}
 
@@ -113,8 +131,12 @@ public:
 		// Running it four times should be enough for these tests.
 		for (unsigned i = 0; i < 4; ++i)
 		{
-			eth::ControlFlowGraph cfg(output);
-			output = cfg.optimisedItems();
+			ControlFlowGraph cfg(output);
+			AssemblyItems optItems;
+			for (BasicBlock const& block: cfg.optimisedBlocks())
+				copy(output.begin() + block.begin, output.begin() + block.end,
+					 back_inserter(optItems));
+			output = move(optItems);
 		}
 		BOOST_CHECK_EQUAL_COLLECTIONS(_expectation.begin(), _expectation.end(), output.begin(), output.end());
 	}
@@ -231,7 +253,8 @@ BOOST_AUTO_TEST_CASE(function_calls)
 
 BOOST_AUTO_TEST_CASE(cse_intermediate_swap)
 {
-	eth::CommonSubexpressionEliminator cse;
+	eth::KnownState state;
+	eth::CommonSubexpressionEliminator cse(state);
 	AssemblyItems input{
 		Instruction::SWAP1, Instruction::POP, Instruction::ADD, u256(0), Instruction::SWAP1,
 		Instruction::SLOAD, Instruction::SWAP1, u256(100), Instruction::EXP, Instruction::SWAP1,
@@ -754,6 +777,30 @@ BOOST_AUTO_TEST_CASE(cse_sha3_twice_same_content_noninterfering_store_in_between
 	BOOST_CHECK_EQUAL(1, count(output.begin(), output.end(), AssemblyItem(Instruction::SHA3)));
 }
 
+BOOST_AUTO_TEST_CASE(cse_with_initially_known_stack)
+{
+	eth::KnownState state = createInitialState(AssemblyItems{
+		u256(0x12),
+		u256(0x20),
+		Instruction::ADD
+	});
+	AssemblyItems input{
+		u256(0x12 + 0x20)
+	};
+	checkCSE(input, AssemblyItems{Instruction::DUP1}, state);
+}
+
+BOOST_AUTO_TEST_CASE(cse_equality_on_initially_known_stack)
+{
+	eth::KnownState state = createInitialState(AssemblyItems{Instruction::DUP1});
+	AssemblyItems input{
+		Instruction::EQ
+	};
+	AssemblyItems output = getCSE(input, state);
+	// check that it directly pushes 1 (true)
+	BOOST_CHECK(find(output.begin(), output.end(), AssemblyItem(u256(1))) != output.end());
+}
+
 BOOST_AUTO_TEST_CASE(control_flow_graph_remove_unused)
 {
 	// remove parts of the code that are unused