sleep experts! Does this signal an improved nights sleep or quite the opposite?

[FlossALumpOfPud]

I've been struggling with DD's sleeping. She is a light sleeper and at 15 weeks is waking three times a night. Not awful I know, i'd like it to be better but can live with it! The main problems have been that she naps so little during the day - half an hour naps about 5 times a day - nothing for love nor money will get her back to sleep properly after that first waking. Problem no 2 that during night time wakings she is up for 1-2hrs once a night.

To try and resolve this I have been doing two things - feeding every three hours as before she was feeding she was going 3-4 hrs between feeds so this was to make sure she gets an 'extra' feed during the day IYSWIM, and getting up at 7 every morning (it was often later) and going to bed at 7 every night, as some nights she was so knackered from lack of naps she'd be asleep before 6pm - perhaps perpetrating the night time wide awake times.

Since we have still been up two to three times during the night. Yesterday for the first time she napped for about 3 hrs in the morning. Nothing more all day. Today however she has had about 2.5hrs this morning and 2.5hrs of (fitful) sleep so far this afternoon. She's still there atm! The long and short of what I'd like to know is if I'm right in thinking improved napping will lead to better nights sleeping?

[FlossALumpOfPud]

oh, and I'm not usually a fan of instigating routine, never did with DS other than a bed time and didn't attempt with dd until last week, but she has been very miserable though overtiredness.