diff --git a/src/terminal/parser/stateMachine.cpp b/src/terminal/parser/stateMachine.cpp
index a9f0dcce..4e360e8c 100644
--- a/src/terminal/parser/stateMachine.cpp
+++ b/src/terminal/parser/stateMachine.cpp
@@ -456,7 +456,7 @@ void StateMachine::_ActionIgnore() noexcept
 // - wch - Character to collect.
 // Return Value:
 // - <none>
-void StateMachine::_ActionOscParam(const wchar_t wch)
+void StateMachine::_ActionOscParam(const wchar_t wch) noexcept
 {
     _trace.TraceOnAction(L"OscParamCollect");
 
@@ -1002,7 +1002,7 @@ void StateMachine::_EventCsiParam(const wchar_t wch)
 // - wch - Character that triggered the event
 // Return Value:
 // - <none>
-void StateMachine::_EventOscParam(const wchar_t wch)
+void StateMachine::_EventOscParam(const wchar_t wch) noexcept
 {
     _trace.TraceOnEvent(L"OscParam");
     if (_isOscTerminator(wch))
@@ -1416,20 +1416,21 @@ void StateMachine::ResetState() noexcept
 //   into the given size_t. All existing value is moved up by 10.
 // - For example, if your value had 437 and you put in the printable number 2,
 //   this function will update value to 4372.
-// - Clamps to size_t max if it gets too big.
+// - Clamps to 32767 if it gets too big.
 // Arguments:
 // - wch - Printable character to accumulate into the value (after conversion to number, of course)
 // - value - The value to update with the printable character. See example above.
 // Return Value:
 // - <none> - But really it's the update to the given value parameter.
-void StateMachine::_AccumulateTo(const wchar_t wch, size_t& value)
+void StateMachine::_AccumulateTo(const wchar_t wch, size_t& value) noexcept
 {
     const size_t digit = wch - L'0';
 
-    // If we overflow while multiplying and adding, the value is just size_t max.
-    if (FAILED(SizeTMult(value, 10, &value)) ||
-        FAILED(SizeTAdd(value, digit, &value)))
+    value = value * 10 + digit;
+
+    // Values larger than the maximum should be mapped to the largest supported value.
+    if (value > MAX_PARAMETER_VALUE)
     {
-        value = std::numeric_limits<size_t>().max();
+        value = MAX_PARAMETER_VALUE;
     }
 }
diff --git a/src/terminal/parser/stateMachine.hpp b/src/terminal/parser/stateMachine.hpp
index ef81387d..5735e751 100644
--- a/src/terminal/parser/stateMachine.hpp
+++ b/src/terminal/parser/stateMachine.hpp
@@ -21,6 +21,12 @@ Module Name:
 
 namespace Microsoft::Console::VirtualTerminal
 {
+    // The DEC STD 070 reference recommends supporting up to at least 16384 for
+    // parameter values, so 32767 should be more than enough. At most we might
+    // want to increase this to 65535, since that is what XTerm and VTE support,
+    // but for now 32767 is the safest limit for our existing code base.
+    constexpr size_t MAX_PARAMETER_VALUE = 32767;
+
     class StateMachine final
     {
 #ifdef UNIT_TESTING
@@ -49,7 +55,7 @@ namespace Microsoft::Console::VirtualTerminal
         void _ActionCollect(const wchar_t wch);
         void _ActionParam(const wchar_t wch);
         void _ActionCsiDispatch(const wchar_t wch);
-        void _ActionOscParam(const wchar_t wch);
+        void _ActionOscParam(const wchar_t wch) noexcept;
         void _ActionOscPut(const wchar_t wch);
         void _ActionOscDispatch(const wchar_t wch);
         void _ActionSs3Dispatch(const wchar_t wch);
@@ -77,13 +83,13 @@ namespace Microsoft::Console::VirtualTerminal
         void _EventCsiIntermediate(const wchar_t wch);
         void _EventCsiIgnore(const wchar_t wch);
         void _EventCsiParam(const wchar_t wch);
-        void _EventOscParam(const wchar_t wch);
+        void _EventOscParam(const wchar_t wch) noexcept;
         void _EventOscString(const wchar_t wch);
         void _EventOscTermination(const wchar_t wch);
         void _EventSs3Entry(const wchar_t wch);
         void _EventSs3Param(const wchar_t wch);
 
-        void _AccumulateTo(const wchar_t wch, size_t& value);
+        void _AccumulateTo(const wchar_t wch, size_t& value) noexcept;
 
         enum class VTStates
         {
diff --git a/src/terminal/parser/ut_parser/OutputEngineTest.cpp b/src/terminal/parser/ut_parser/OutputEngineTest.cpp
index f5228454..05045ecc 100644
--- a/src/terminal/parser/ut_parser/OutputEngineTest.cpp
+++ b/src/terminal/parser/ut_parser/OutputEngineTest.cpp
@@ -525,7 +525,7 @@ class Microsoft::Console::VirtualTerminal::OutputEngineTest final
             mach.ProcessCharacter(wch);
             VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscParam);
         }
-        VERIFY_ARE_EQUAL(mach._oscParameter, sizeMax);
+        VERIFY_ARE_EQUAL(mach._oscParameter, MAX_PARAMETER_VALUE);
         mach.ProcessCharacter(L';');
         VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscString);
         mach.ProcessCharacter(L's');
@@ -542,7 +542,7 @@ class Microsoft::Console::VirtualTerminal::OutputEngineTest final
             mach.ProcessCharacter(wch);
             VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscParam);
         }
-        VERIFY_ARE_EQUAL(mach._oscParameter, sizeMax);
+        VERIFY_ARE_EQUAL(mach._oscParameter, MAX_PARAMETER_VALUE);
         mach.ProcessCharacter(L';');
         VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscString);
         mach.ProcessCharacter(L's');
@@ -1064,15 +1064,20 @@ class StateMachineExternalTest final
     void ApplyParameterBoundary(size_t* uiExpected, size_t uiGiven)
     {
         // 0 and 1 should be 1. Use the preset value.
-        // 2019-12: No longer bound by SHORT_MAX. Goes all the way to size_t.
+        // 1-MAX_PARAMETER_VALUE should be what we set.
+        // > MAX_PARAMETER_VALUE should be MAX_PARAMETER_VALUE.
         if (uiGiven <= 1)
         {
             *uiExpected = 1u;
         }
-        else if (uiGiven > 1)
+        else if (uiGiven > 1 && uiGiven <= MAX_PARAMETER_VALUE)
         {
             *uiExpected = uiGiven;
         }
+        else if (uiGiven > MAX_PARAMETER_VALUE)
+        {
+            *uiExpected = MAX_PARAMETER_VALUE; // 32767 is our max value.
+        }
     }
 
     void TestCsiCursorMovement(wchar_t const wchCommand,