I don't recall if this rule is in SR4a, but it is definitely in SR4.
Your starting Notoriety is modified by various positive and negative qualities. Each positive quality subtracts one from your notoriety, while each negative quality adds on.
Positive Qualities
Blandness
First Impression
Lucky
Negative Qualities
Addiction
Bad Luck
Combat Paralysis
Elf Poser
Gremlins
Incompetent
Infirm
Ork Poser
Scorched
SINer (Criminal Only)
Spirit Bane
Uncouth
Uneducated
Runner's Companion doesn't indicate which new qualities add or subtract from starting notoriety. I've gone through and assembled a list of which ones I think would affect it.
For positive qualities, I noted that two of the three were social related, either the person was favorably held, or it decreased their visibility.
Common Sense - The quality itself seems fuzzy at best, and a runner that is known for common sense probably shouldn't have as high a notoriety.
Digital Doppleganger - Similar to Blandness.
Erased - Similar to Blandness.
Escaped Clone - Similar to Blandness
Fame - Similar to First Impression
Mistaken Identity - Similar to First Impression and Blandness.
For negative qualities, it appeared that most of them were really a stain on the character, a bad behavior or just something that causes constant problems. A lot of the new negative qualities I think could be added to increase starting notoriety.
Bi-Polar
Computer Illiterate - Worse than incompetent.
Enemy
Evil Twin
Hung Out to Dry
Illiterate
Liar
Mental Handicap
Paraplegic
Poor Self Control (Braggart)
Poor Self Control (Compulsive (10/15BP version only))
Prejudiced (10/15BP degree only)
Quadriplegic
Signature
Vendetta
Wanted
Looking for comments, I would like to get a good list.