I have read that one of the tradeoffs for adding table indexes in SQL Server is the increased cost of insert/update/delete queries to benefit the performance of select queries.

I can conceptually understand what happens in the case of an insert because SQL Server has to write entries into each index matching the new rows, but update and delete are a little more murky to me because I can't quite wrap my head around what the database engine has to do.

Let's take DELETE as an example and assume I have the following schema (pardon the pseudo-SQL)

TABLE Foo
 col1 int
,col2 int
,col3 int
,col4 int
PRIMARY KEY (col1,col2)

INDEX IX_1
col3
INCLUDE 
col4

Now, if I issue the statement

DELETE FROM Foo WHERE col1=12 AND col2 > 34

I understand what the engine must do to update the table (or clustered index if you prefer). The index is set up to make it easy to find the range of rows to be removed and do so.

However, at this point it also needs to update IX_1 and the query that I gave it gives no obvious efficient way for the database engine to find the rows to update. Is it forced to do a full index scan at this point? Does the engine read the rows from the clustered index first and generate a smarter internal delete against the index?

It might help me to wrap my head around this if I understood better what is going on under the hood, but I guess my real question is this. I have a database that is spending a significant amount of time in delete and I'm trying to figure out what I can do about it.

When I display the execution plan for the deletion, it just shows an entry for "Clustered Index Delete" on table Foo which lists in the details section the other indices that need to be updated but I don't get any indication of the relative cost of these other indices.

Are they all equal in this case? Is there some way that I can estimate the impact of removing one or more of these indices without having to actually try it?