diff --git a/crates/hyperdrive-math/src/lib.rs b/crates/hyperdrive-math/src/lib.rs
index 887fa86b..c5600c43 100644
--- a/crates/hyperdrive-math/src/lib.rs
+++ b/crates/hyperdrive-math/src/lib.rs
@@ -161,7 +161,7 @@ impl State {
 
     /// Calculates the pool reserve levels to achieve a target interest rate.
     /// This calculation does not take into account Hyperdrive's solvency
-    /// constraints, share adjustments, or exposure and shouldn't be used
+    /// constraints or exposure and shouldn't be used
     /// directly.
     ///
     /// The price for a given fixed-rate is given by
@@ -177,7 +177,7 @@ impl State {
     /// For a target rate, `$r_t$`, the pool share reserves, `$z_t$`, must be:
     ///
     /// ```math
-    /// z_t = \frac{1}{\mu} \left(
+    /// z_t = \zeta + \frac{1}{\mu} \left(
     ///   \frac{k}{\frac{c}{\mu} + \left(
     ///     (r_t \cdot t + 1)^{\frac{1}{t_s}}
     ///   \right)^{1 - t_{s}}}
@@ -208,7 +208,10 @@ impl State {
         let inner = (self.k_down()?
             / (c_over_mu + scaled_rate.pow(fixed!(1e18) - self.time_stretch())?))
         .pow(fixed!(1e18) / (fixed!(1e18) - self.time_stretch()))?;
-        let target_share_reserves = inner / self.initial_vault_share_price();
+        let target_effective_share_reserves = inner / self.initial_vault_share_price();
+        let target_share_reserves = FixedPoint::try_from(
+            I256::try_from(target_effective_share_reserves)? + self.share_adjustment(),
+        )?;
 
         // Then get the target bond reserves.
         let target_bond_reserves = inner * scaled_rate;
diff --git a/crates/hyperdrive-math/src/long/targeted.rs b/crates/hyperdrive-math/src/long/targeted.rs
index 9a7863d3..3d9b9f77 100644
--- a/crates/hyperdrive-math/src/long/targeted.rs
+++ b/crates/hyperdrive-math/src/long/targeted.rs
@@ -51,7 +51,7 @@ impl State {
         let checkpoint_exposure = checkpoint_exposure.into();
         let allowable_error = match maybe_allowable_error {
             Some(allowable_error) => allowable_error.into(),
-            None => fixed!(1e14),
+            None => fixed!(1e15),
         };
         let current_rate = self.calculate_spot_rate()?;
         if target_rate >= current_rate {