diff --git a/src/consolidations/ctor.eas b/src/consolidations/ctor.eas
index 76e5f4f..180f8d3 100644
--- a/src/consolidations/ctor.eas
+++ b/src/consolidations/ctor.eas
@@ -1,7 +1,7 @@
-;; Store 1181 as a temporary excess value as it creates a fee so large that no
+;; Store 16384 as a temporary excess value as it creates a fee so large that no
 ;; request will be accepted in the queue until after 7002 is activated and
 ;; called by the system for the first time.
-push 1181
+push 16384
 push0
 sstore
 
diff --git a/src/consolidations/main.eas b/src/consolidations/main.eas
index b082e3a..d176d3f 100644
--- a/src/consolidations/main.eas
+++ b/src/consolidations/main.eas
@@ -24,7 +24,7 @@
 #define TARGET_PER_BLOCK 1
 #define MAX_PER_BLOCK 1
 #define FEE_UPDATE_FRACTION 17
-#define EXCESS_INHIBITOR 1181
+#define EXCESS_INHIBITOR 16384
 
 #define INPUT_SIZE 96    ;; the size of (source ++ target)
 #define RECORD_SIZE 116  ;; the size of (address ++ source ++ target)
diff --git a/src/withdrawals/ctor.eas b/src/withdrawals/ctor.eas
index 76e5f4f..180f8d3 100644
--- a/src/withdrawals/ctor.eas
+++ b/src/withdrawals/ctor.eas
@@ -1,7 +1,7 @@
-;; Store 1181 as a temporary excess value as it creates a fee so large that no
+;; Store 16384 as a temporary excess value as it creates a fee so large that no
 ;; request will be accepted in the queue until after 7002 is activated and
 ;; called by the system for the first time.
-push 1181
+push 16384
 push0
 sstore
 
diff --git a/src/withdrawals/main.eas b/src/withdrawals/main.eas
index b109751..6e497f2 100644
--- a/src/withdrawals/main.eas
+++ b/src/withdrawals/main.eas
@@ -34,7 +34,7 @@
 #define TARGET_PER_BLOCK 2
 #define MAX_PER_BLOCK 16
 #define FEE_UPDATE_FRACTION 17
-#define EXCESS_INHIBITOR 1181
+#define EXCESS_INHIBITOR 16384
 
 #define INPUT_SIZE 56   ;; the size of (pubkey ++ amount)
 #define RECORD_SIZE 76  ;; the size of (address ++ pubkey ++ amount)
diff --git a/test/Consolidation.t.sol.in b/test/Consolidation.t.sol.in
index f779ea6..2142011 100644
--- a/test/Consolidation.t.sol.in
+++ b/test/Consolidation.t.sol.in
@@ -146,15 +146,15 @@ contract ConsolidationTest is Test {
   // testInhibitorRest verifies that after the first system call the excess
   // value is reset to 0.
   function testInhibitorReset() public {
-    vm.store(addr, bytes32(0), bytes32(uint256(1181)));
+    vm.store(addr, bytes32(0), bytes32(uint256(16384)));
     vm.prank(sysaddr);
     (bool ret, bytes memory data) = addr.call("");
     assertStorage(excess_slot, 0, "expected excess requests to be reset");
 
-    vm.store(addr, bytes32(0), bytes32(uint256(1180)));
+    vm.store(addr, bytes32(0), bytes32(uint256(16383)));
     vm.prank(sysaddr);
     (ret, data) = addr.call("");
-    assertStorage(excess_slot, 1180-target_per_block, "didn't expect excess to be reset");
+    assertStorage(excess_slot, 16383-target_per_block, "didn't expect excess to be reset");
   }
 
   // --------------------------------------------------------------------------
diff --git a/test/FakeExpo.t.sol.in b/test/FakeExpo.t.sol.in
index 2a12229..7c1a70a 100644
--- a/test/FakeExpo.t.sol.in
+++ b/test/FakeExpo.t.sol.in
@@ -11,5 +11,6 @@ contract FakeExpoTest is Test {
   // testFakeExpo calls the fake exponentiation logic with specific values.
   function testFakeExpo() public {
     assertEq(callFakeExpo(1, 100, 17), 357);
+    assertEq(callFakeExpo(1, 16384, 17), 550585409188229536592656984201962691914788118703985791268517117099222302069);
   }
 }
diff --git a/test/Withdrawal.t.sol.in b/test/Withdrawal.t.sol.in
index 7d66895..33dee4a 100644
--- a/test/Withdrawal.t.sol.in
+++ b/test/Withdrawal.t.sol.in
@@ -144,15 +144,15 @@ contract WithdrawalsTest is Test {
   // testInhibitorRest verifies that after the first system call the excess
   // value is reset to 0.
   function testInhibitorReset() public {
-    vm.store(addr, bytes32(0), bytes32(uint256(1181)));
+    vm.store(addr, bytes32(0), bytes32(uint256(16384)));
     vm.prank(sysaddr);
     (bool ret, bytes memory data) = addr.call("");
     assertStorage(excess_slot, 0, "expected excess requests to be reset");
 
-    vm.store(addr, bytes32(0), bytes32(uint256(1180)));
+    vm.store(addr, bytes32(0), bytes32(uint256(16383)));
     vm.prank(sysaddr);
     (ret, data) = addr.call("");
-    assertStorage(excess_slot, 1180-target_per_block, "didn't expect excess to be reset");
+    assertStorage(excess_slot, 16383-target_per_block, "didn't expect excess to be reset");
   }
 
   // --------------------------------------------------------------------------