diff --git a/libyul/optimiser/KnowledgeBase.cpp b/libyul/optimiser/KnowledgeBase.cpp
index 2fd5fb0a9..23627653a 100644
--- a/libyul/optimiser/KnowledgeBase.cpp
+++ b/libyul/optimiser/KnowledgeBase.cpp
@@ -33,6 +33,11 @@ using namespace std;
 using namespace solidity;
 using namespace solidity::yul;
 
+KnowledgeBase::KnowledgeBase(map<YulString, AssignedValue> const& _ssaValues):
+	m_valuesAreSSA(true),
+	m_variableValues([_ssaValues](YulString _var) { return util::valueOrNullptr(_ssaValues, _var); })
+{}
+
 bool KnowledgeBase::knownToBeDifferent(YulString _a, YulString _b)
 {
 	if (optional<u256> difference = differenceIfKnownConstant(_a, _b))
@@ -85,11 +90,23 @@ optional<u256> KnowledgeBase::valueIfKnownConstant(Expression const& _expression
 
 KnowledgeBase::VariableOffset KnowledgeBase::explore(YulString _var)
 {
-	// We query the value first so that the variable is reset if it has changed
-	// since the last call.
-	Expression const* value = valueOf(_var);
-	if (VariableOffset const* varOff = util::valueOrNullptr(m_offsets, _var))
-		return *varOff;
+	Expression const* value = nullptr;
+	if (m_valuesAreSSA)
+	{
+		// In SSA, a once determined offset is always valid, so we first see
+		// if we already computed it.
+		if (VariableOffset const* varOff = util::valueOrNullptr(m_offsets, _var))
+			return *varOff;
+		value = valueOf(_var);
+	}
+	else
+	{
+		// For non-SSA, we query the value first so that the variable is reset if it has changed
+		// since the last call.
+		value = valueOf(_var);
+		if (VariableOffset const* varOff = util::valueOrNullptr(m_offsets, _var))
+			return *varOff;
+	}
 
 	if (value)
 		if (optional<VariableOffset> offset = explore(*value))
@@ -129,9 +146,12 @@ optional<KnowledgeBase::VariableOffset> KnowledgeBase::explore(Expression const&
 
 Expression const* KnowledgeBase::valueOf(YulString _var)
 {
-	Expression const* lastValue = m_lastKnownValue[_var];
 	AssignedValue const* assignedValue = m_variableValues(_var);
 	Expression const* currentValue = assignedValue ? assignedValue->value : nullptr;
+	if (m_valuesAreSSA)
+		return currentValue;
+
+	Expression const* lastValue = m_lastKnownValue[_var];
 	if (lastValue != currentValue)
 		reset(_var);
 	m_lastKnownValue[_var] = currentValue;
@@ -140,6 +160,8 @@ Expression const* KnowledgeBase::valueOf(YulString _var)
 
 void KnowledgeBase::reset(YulString _var)
 {
+	yulAssert(!m_valuesAreSSA);
+
 	m_lastKnownValue.erase(_var);
 	if (VariableOffset const* offset = util::valueOrNullptr(m_offsets, _var))
 	{
diff --git a/libyul/optimiser/KnowledgeBase.h b/libyul/optimiser/KnowledgeBase.h
index 82c82a7e9..934b2e21a 100644
--- a/libyul/optimiser/KnowledgeBase.h
+++ b/libyul/optimiser/KnowledgeBase.h
@@ -47,6 +47,9 @@ struct AssignedValue;
  * form.
  * The only requirement is that the assigned values are movable expressions.
  *
+ * There is a constructor to provide all SSA values right at the beginning.
+ * If you use this, the KnowledgeBase will be slightly more efficient.
+ *
  * Internally, tries to find groups of variables that have a mutual constant
  * difference and stores these differences always relative to a specific
  * representative variable of the group.
@@ -57,9 +60,13 @@ struct AssignedValue;
 class KnowledgeBase
 {
 public:
+	/// Constructor for arbitrary value callback that allows for variable values
+	/// to change in between calls to functions of this class.
 	KnowledgeBase(std::function<AssignedValue const*(YulString)> _variableValues):
 		m_variableValues(std::move(_variableValues))
 	{}
+	/// Constructor to use if source code is in SSA form and values are constant.
+	KnowledgeBase(std::map<YulString, AssignedValue> const& _ssaValues);
 
 	bool knownToBeDifferent(YulString _a, YulString _b);
 	std::optional<u256> differenceIfKnownConstant(YulString _a, YulString _b);
@@ -91,6 +98,8 @@ private:
 
 	VariableOffset setOffset(YulString _variable, VariableOffset _value);
 
+	/// If true, we can assume that variable values never change and skip some steps.
+	bool m_valuesAreSSA = false;
 	/// Callback to retrieve the current value of a variable.
 	std::function<AssignedValue const*(YulString)> m_variableValues;
 
diff --git a/libyul/optimiser/UnusedStoreEliminator.cpp b/libyul/optimiser/UnusedStoreEliminator.cpp
index 245533395..3df9c6319 100644
--- a/libyul/optimiser/UnusedStoreEliminator.cpp
+++ b/libyul/optimiser/UnusedStoreEliminator.cpp
@@ -104,7 +104,7 @@ UnusedStoreEliminator::UnusedStoreEliminator(
 	m_functionSideEffects(_functionSideEffects),
 	m_controlFlowSideEffects(_controlFlowSideEffects),
 	m_ssaValues(_ssaValues),
-	m_knowledgeBase([this](YulString _var) { return util::valueOrNullptr(m_ssaValues, _var); })
+	m_knowledgeBase(_ssaValues)
 {}
 
 void UnusedStoreEliminator::operator()(FunctionCall const& _functionCall)