Default Bluetooth Mouse is lagging/stuttering

Hi folks,
My A4tech BT-630B behaves rather strangely when connected to Note 3 9005 (Android 4.3, MJ7, not rooted yet). Though there's no problem with connection/disconnecting the mouse, the pointer on screen has a significant lag and becomes virtually unusable.

I've had no problems with this mouse on any other devices (including Win tablets, Android 4.2.2 phones etc). I've tried switching off Wi-Fi, setting bluetooth visibility timeout, and connecting/disconecting together with other bluetooth devices with no luck so far. Again, strangely enough bluetooth headset and keyboard work perfectly (no double letter or anything). Just this damn pointer ruins everything. So, I'd really appreciate your input on this.