[quote=pabloesqobar]Is there a written lease? Verbal lease? What are the terms? Month to month or a fixed period?

If you want to make a case for non-payment, DO NOT CASH/ACCEPT the check for the lesser amount. The future Defendants will use your acceptance of that amount as contractually agreeing to the next month at that rate. Once you cash it, you’ve basically agreed to that rate.

If your goal is to get rid of that tenant, do not cash the check. Give the 3 day notice. Use the expedited procedure that exists for unlawful detainer cases.[/quote]
Seriously.
Do not accept a lesser amount.
Once you accept it…well..you’ve accepted it.
In court the tenant can always claim “well, I just kept paying the rent like always and some guest must have signed for the letter…”.

Here is an excerpt from Nolo’s “First Time Landlord” book on the legal aspects of eviction:

“If you accept even a partial amount of rent a tenant owes–whether for past months or even just the current month–you will, in moist states, cancel the effect of a Pay Rent or Quit notice.”

You can issue a new notice for the new amount after accepting some small amount but then they give you another small amount and so on.

Also, the Nolo books are worth buying. Even as a kindle version.