DSum, Specific Links Or Anything Else?

Dear all, imagine a table named "Database" with fields

Par1, Par2, ... ParN, Amount,

where most of the parameters in Par1,...ParN are in text format.
The structure of another table, "Criteria", is exactly like "Database" less "Amount" field.
Suppose we want to summarise "Amounts" from "Database" according to the sets of "Criteria", for each of its records. A set does not always include all of the fields, e.g. an empty field (or sort of wildcard) may mean that any value fits.
It seems like classical application of DSum function, but I've already spent a lot of time in desperate attempts to solve this problem and will highly appreciate your suggestions.