You can do one thing. While making the gif image . Remove unwanted blank spaces. Avoid much colors and keep the size small.

You can make gif images using softwares like Coffee cup gif maker, Active Gif maker etc.

A freeware tool is Unfreez . very easy to use and is small in size.
GO to http://www.whitsoftdev.com/unfreez/ to download it.
After downloading , just choose the images which you want to repeat after one another and click on ANIMATE GIF to get your own Gif image . A very easy task !

The following links are where you can find tutorials for creating gif images.

http://members.aol.com/royalef/gifmake.htm
http://www.bobpowell.net/giftransparency.htm
http://www.devx.com/projectcool/Article/19997/1954?pf=true
http://www.frontiernet.net/~steve_glimpse/anidraw.html
http://www.htmltutorials.ca/lesson15.htm
http://www.infocellar.com/Graphics/16-color.htm

CONCEPT BEHIND GIF IMAGES : Gif images are nothing but a series of images which come one after the other. You can set the time delay for each image.

Another easy explanation : It is done by creating a series of gif images and then displaying them in sequence.

You can even create Gif images using Adobe image ready which comes with Photoshop.

Try GIF Construction Set Professional from Alchemy Mindworks.