It's all in the maths 
The calorie deficit you need to lose 1kg (2.2lb) is 7500. So if you know your basal metabolic rate (BMR - google for BMR calculators), which tells you how many calories a day you need just to 'be' then you can work out how many calories you have to eat/need to exercise to get to this 7500 deficit. If you can get a greater deficit then you will lose more weight.
For example, say you are an 11 stone woman about 5' 2" in height. Your BMR will be about 1500 cals. Add about 300 for incidental exercise, such as walking to the car, around the supermarket etc and you have about 1800 calories to spend.
If you do 300 calories of exercise a day, and only eat 1200 calories, then you have a daily deficit of 600. Do this every day and you have a deficit of 7x600 = 4200. You would need a deficit of an additional 3,300 calories to reach the 2.2lb mark.
To do this you would either need to exercise more, eat less or change your body composition to burn more energy (build muscle).
So, looking at it that way 2lb is actually pretty good going! Often the dramatic movements on the scale are due to water, not fat.
Incidentally, crash diets can slow down your BMR, so that's why they are not a good idea.