diff --git a/src/terminal/parser/stateMachine.cpp b/src/terminal/parser/stateMachine.cpp
index 432d287ce0..79ed50a03f 100644
--- a/src/terminal/parser/stateMachine.cpp
+++ b/src/terminal/parser/stateMachine.cpp
@@ -450,12 +450,16 @@ void StateMachine::_ActionParam(const wchar_t wch)
                 // multiply existing values by 10 to make space in the 1s digit
                 *_pusActiveParam *= 10;
 
-                // mark that we've now stored another digit.
-                _iParamAccumulatePos++;
-
                 // store the digit in the 1s place.
                 *_pusActiveParam += usDigit;
 
+                // if the total is zero, it must be a leading zero digit, so we don't count it.
+                if (*_pusActiveParam != 0)
+                {
+                    // otherwise mark that we've now stored another digit.
+                    _iParamAccumulatePos++;
+                }
+
                 if (*_pusActiveParam > SHORT_MAX)
                 {
                     *_pusActiveParam = SHORT_MAX;
@@ -530,12 +534,16 @@ void StateMachine::_ActionOscParam(const wchar_t wch)
         // multiply existing values by 10 to make space in the 1s digit
         _sOscParam *= 10;
 
-        // mark that we've now stored another digit.
-        _iParamAccumulatePos++;
-
         // store the digit in the 1s place.
         _sOscParam += usDigit;
 
+        // if the total is zero, it must be a leading zero digit, so we don't count it.
+        if (_sOscParam != 0)
+        {
+            // otherwise mark that we've now stored another digit.
+            _iParamAccumulatePos++;
+        }
+
         if (_sOscParam > SHORT_MAX)
         {
             _sOscParam = SHORT_MAX;
diff --git a/src/terminal/parser/ut_parser/OutputEngineTest.cpp b/src/terminal/parser/ut_parser/OutputEngineTest.cpp
index 15e423fff6..84fed5c355 100644
--- a/src/terminal/parser/ut_parser/OutputEngineTest.cpp
+++ b/src/terminal/parser/ut_parser/OutputEngineTest.cpp
@@ -273,6 +273,30 @@ class Microsoft::Console::VirtualTerminal::OutputEngineTest final
         VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Ground);
     }
 
+    TEST_METHOD(TestLeadingZeroCsiParam)
+    {
+        StateMachine mach(new OutputStateMachineEngine(new DummyDispatch));
+
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Ground);
+        mach.ProcessCharacter(AsciiChars::ESC);
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Escape);
+        mach.ProcessCharacter(L'[');
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::CsiEntry);
+        for (int i = 0; i < 50; i++) // Any number of leading zeros should be supported
+        {
+            mach.ProcessCharacter(L'0');
+            VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::CsiParam);
+        }
+        for (int i = 0; i < 5; i++) // We're only expecting to be able to keep 5 digits max
+        {
+            mach.ProcessCharacter((wchar_t)(L'1' + i));
+            VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::CsiParam);
+        }
+        VERIFY_ARE_EQUAL(*mach._pusActiveParam, 12345);
+        mach.ProcessCharacter(L'J');
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Ground);
+    }
+
     TEST_METHOD(TestCsiIgnore)
     {
         StateMachine mach(new OutputStateMachineEngine(new DummyDispatch));
@@ -429,6 +453,35 @@ class Microsoft::Console::VirtualTerminal::OutputEngineTest final
         mach.ProcessCharacter(AsciiChars::BEL);
         VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Ground);
     }
+
+    TEST_METHOD(TestLeadingZeroOscParam)
+    {
+        StateMachine mach(new OutputStateMachineEngine(new DummyDispatch));
+
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Ground);
+        mach.ProcessCharacter(AsciiChars::ESC);
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Escape);
+        mach.ProcessCharacter(L']');
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscParam);
+        for (int i = 0; i < 50; i++) // Any number of leading zeros should be supported
+        {
+            mach.ProcessCharacter(L'0');
+            VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscParam);
+        }
+        for (int i = 0; i < 5; i++) // We're only expecting to be able to keep 5 digits max
+        {
+            mach.ProcessCharacter((wchar_t)(L'1' + i));
+            VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscParam);
+        }
+        VERIFY_ARE_EQUAL(mach._sOscParam, 12345);
+        mach.ProcessCharacter(L';');
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscString);
+        mach.ProcessCharacter(L's');
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::OscString);
+        mach.ProcessCharacter(AsciiChars::BEL);
+        VERIFY_ARE_EQUAL(mach._state, StateMachine::VTStates::Ground);
+    }
+
     TEST_METHOD(TestLongOscParam)
     {
         StateMachine mach(new OutputStateMachineEngine(new DummyDispatch));