diff --git a/test/invariant/Invariants.t.sol b/test/invariant/Invariants.t.sol
index 5f67a3b..f0ff9ee 100644
--- a/test/invariant/Invariants.t.sol
+++ b/test/invariant/Invariants.t.sol
@@ -85,11 +85,11 @@ abstract contract PSMInvariantTestBase is PSMTestBase {
 
         // LPs position value can increase from transfers into the PSM and from swapping rounding
         // errors increasing the value of the PSM slightly.
-        // Allow a 4 tolerance for negative rounding on conversion calculations.
-        assertGe(lpAssetValue + 1e12, lpDeposits);
+        // Allow a 2e12 tolerance for negative rounding on conversion calculations.
+        assertGe(lpAssetValue + 2e12, lpDeposits);
 
-        // Include seed deposit, allow for 1e12 negative tolerance.
-        assertGe(psm.getPsmTotalValue() + 1e12, lpDeposits);
+        // Include seed deposit, allow for 2e12 negative tolerance.
+        assertGe(psm.getPsmTotalValue() + 2e12, lpDeposits);
     }
 
     function _checkInvariant_E() public view {
diff --git a/test/invariant/handlers/SwapperHandler.sol b/test/invariant/handlers/SwapperHandler.sol
index 9eec1a6..150b5cc 100644
--- a/test/invariant/handlers/SwapperHandler.sol
+++ b/test/invariant/handlers/SwapperHandler.sol
@@ -138,13 +138,16 @@ contract SwapperHandler is HandlerBase {
             "SwapperHandler/swap/conversion-rate-million-decrease"
         );
 
-        // Position values can fluctuate by up to 0.00000002% on swaps
-        assertApproxEqRel(
-            psm.convertToAssetValue(psm.shares(lp0)),
-            startingConversionLp0,
-            0.000002e18,
-            "SwapperHandler/swap/conversion-rate-change-lp"
-        );
+        // Disregard this assertion if the LP has less than a dollar of value
+        if (startingConversionLp0 > 1e18) {
+            // Position values can fluctuate by up to 0.00000002% on swaps
+            assertApproxEqRel(
+                psm.convertToAssetValue(psm.shares(lp0)),
+                startingConversionLp0,
+                0.000002e18,
+                "SwapperHandler/swap/conversion-rate-change-lp"
+            );
+        }
 
         // Decrease in value from rounding is capped at 2e12
         assertGe(