Two ways, but first figure out what the dizziness feeling is or at least make sure your training with someone else who knows they need to keep an eye on you. I cant think of a time I was dizzy after stopping fast, so that would scare me. So you know, to compare, my heart rate doesn't drop too fast after a certain point. After training at 160 bpm it will drop to 130 quickly then 110 after 30-60 seconds maybe then down lower over the next 5-10 minutes. My resting heart rate is 45 bpm which is different from most people in the same shape that I am in.
One you should incorporate some high intensity workouts in your routine. Sprint for 10-20 minutes at a time. Go all out for 5-10 minutes. I do this for running so swimming may have a little difference in the timing.
Two you need to find out what low intensity means. You can do this by using heart rate monitors and defining what each zone means. For example, when your entering the aerobic zone this means that your breathing rate is just starting to be more than normal. See the chart here for more reliable information. Another way to do this is by running with someone to help them start out running which will force you to their slower pace, force your self to slow down using a watch, or take very short and slow strides to do a lazy jog.