diff --git a/libraries/AC_AttitudeControl/AC_PosControl.cpp b/libraries/AC_AttitudeControl/AC_PosControl.cpp
index b7a8813dc1..d8ab060c4e 100644
--- a/libraries/AC_AttitudeControl/AC_PosControl.cpp
+++ b/libraries/AC_AttitudeControl/AC_PosControl.cpp
@@ -723,10 +723,9 @@ void AC_PosControl::relax_z_controller(float throttle_setting)
     // Initialise the position controller to the current position, velocity and acceleration.
     init_z_controller();
 
-    // Set accel PID I term based on the requested throttle
-    float throttle = _attitude_control.get_throttle_in();
-    throttle_setting = throttle + (throttle_setting - throttle) * (_dt / (_dt + POSCONTROL_RELAX_TC));
-    _pid_accel_z.set_integrator((throttle_setting - _motors.get_throttle_hover()) * 1000.0f);
+    // init_z_controller has set the accel PID I term to generate the current throttle set point
+    // Use relax_integrator to decay the throttle set point to throttle_setting
+    _pid_accel_z.relax_integrator((throttle_setting - _motors.get_throttle_hover()) * 1000.0f, POSCONTROL_RELAX_TC);
 }
 
 /// init_z_controller - initialise the position controller to the current position, velocity, acceleration and attitude.
@@ -757,7 +756,11 @@ void AC_PosControl::init_z_controller()
     _accel_offset_z = 0.0;
 
     // Set accel PID I term based on the current throttle
-    _pid_accel_z.set_integrator((_attitude_control.get_throttle_in() - _motors.get_throttle_hover()) * 1000.0f);
+    // Remove the expected P term due to _accel_desired.z being constrained to _accel_max_z_cmss
+    // Remove the expected FF term due to non-zero _accel_target.z
+    _pid_accel_z.set_integrator((_attitude_control.get_throttle_in() - _motors.get_throttle_hover()) * 1000.0f
+        - _pid_accel_z.kP() * (_accel_target.z - get_z_accel_cmss())
+        - _pid_accel_z.ff() * _accel_target.z);
 
     // initialise ekf z reset handler
     init_ekf_z_reset();
diff --git a/libraries/AC_AttitudeControl/AC_PosControl.h b/libraries/AC_AttitudeControl/AC_PosControl.h
index ca6ac4ea56..323b313636 100644
--- a/libraries/AC_AttitudeControl/AC_PosControl.h
+++ b/libraries/AC_AttitudeControl/AC_PosControl.h
@@ -34,7 +34,7 @@
 
 #define POSCONTROL_OVERSPEED_GAIN_Z             2.0f    // gain controlling rate at which z-axis speed is brought back within SPEED_UP and SPEED_DOWN range
 
-#define POSCONTROL_RELAX_TC                     0.16f   // This is used to decay the relevant variable to 5% in half a second.
+#define POSCONTROL_RELAX_TC                     0.16f   // This is used to decay the I term to 5% in half a second.
 
 class AC_PosControl
 {