Here is a small survival kit that fits into a 4 inch diameter. I have tried to include as much as possible to get you through minor emergencies and help you light fires/cook, tend to wounds and make minor repairs:

The kit contains the following:

Basic first aid kit,
Disposable lighter,
8 inch cable ties x 4 ,
Duct tape (so many uses - any problem can be solved with duct tape and cable ties ),
15 feet of nylon fishing line,
Small tube of super glue,
Sewing kit with 2 needles, and 20 feet of cotton in black and white,
2 small elastic bands,
Half a hacksaw blade (for small saw jobs),
Cotton wool (good for starting fires),
Sanding board,
Silver foil (for making containers for water to boil on a fire , or for food storage,
Swiss army knife - mine is a small one but has 8 blades including a working pair of scissors,
Salt and Pepper sachet -to season anything you cook,
A tab of laminated paper with your home address on and phone number incase the worst happens and someone finds you,
A Condom for carrying water in.

Step 1: Contents of the First Aid Kit

This is the small first aid kit to cover scratches and bruises, the antiseptic wipe is most important to stop any infections that may happen should you catch yourself on rusty metal or on some dirty water.

3 large plasters - good enough for minor cuts and bruises.
Sterile antiseptic wipe -for cleaning the wounds.
4 safety pins - these can be used for all sorts of things including makeshift fishing hooks.
5 paper clips, good for bending and all sorts of uses - not sure why they are in here but they just are.
needle. This has been included here to remove thorns and splinters, would be heated in the lighters flame to clean it before use.

I also plan to put some headache tablets in here as well as stomach upset tablets,

Step 2: All Packed in the Tin

All the items packed in the tin.

Still plenty of room to put a pencil and paper in there as well if you want to.

Other useful items would be water sterilization tablets (NEVER DRINK DIRTY WATER OR WATER FROM RIVERS AND STREAMS WITHOUT FIRST BOILING OR TREATING IT)

You could also add waterproof matches or replace the lighter with a magnesium fire starter. multiple methods of starting fires are always of benifit.