It's hard to tell based on the info shared and what you consider a good bump
Plus when were these lates on the mortgage and the car, because depending on how recent they are they may have more impact on your current score.
The neg impact imposed by a levy/public record or any neg in general stings less over time but if the lates are 'young' age wise, the bump won't be much because the impact had worn thin to begin with.
I might add, some secured TLs on your reports to age positively as, some of the old negs age the other direction... waiting to add accounts only makes them that much younger in the future. Better to have small TLs building now vs having zero revolving accounts aging...Two $200 credit cards used for gas or Netflix will do the trick.
Couple that with the car and mortgage payment and you've got mixture and are building positive history while baddies age off and you're paying off the car and house anyway.
Keep the usage percentage low and a $200 cards builds a credit history just fine a $40 balance for a gas purchase is 20% of a $200 CL....the computer sees the same % and grades it just the same as a $400 balance. on a $2000 CL credit account.
Good luck
