Vetting tenants - What should you check before letting someone into your property?

In this weekend's FT there was an article about the increase in the level of checking tenants. This is fully undestandable in the current economic environment, but what kinds of checks are appropriate for a tenant?

"Letting agents are putting prospective tenants through rigorous credit checks as property owners want to see proof of income, including bonuses, as well as highly personal information such as the value of investment and share portfolios and savings accounts.
Knight Frank, the agent, said it had reviewed its reference process for new tenants to make sure it could provide enough data for landlords. Rather than using traditional credit checking agencies it is now conducting manual checks itself.
In some cases it is having to procure an indication of the tenants’ net wealth from their banks as well as guarantees from their employers that their jobs are permanent and not under threat, and details of their anticipated bonuses. " states the article in the FT.

Considering that the risk to the landlord is similar -if not greater- to the risk to an employer, then it would only make sense that checks that confirm the likelihood of the tenant remaining in employment should be conducted. Obviously an employer is unlikely to confirm whether they intend to make someone redundant in the near future, but asking the right questions may give you a good indication as to the relative job security of a prospective tenant.