My query worked! Now what?

Recently I sent out a slew of queries and responses are finally trickling in. About half of the packages I sent out included the first 20/50/whatever pages and a synopsis as requested by the agent; the others were simple query letters.

Today I got this response to one of my "query only" mailings:

"Can you please send me the first three chapters and a synopsis of the balance? One caveat, we do ask to review material on an exclusive basis and I hope you will agree."

Okay, first of all, is she referring to an "exclusive basis" in the event that they request the entire manuscript? I've never heard of asking for an exclusive on the synopsis and a sample chapter, which is what it sounds like she wants! Of course if this is the case I have a problem because I've already sent out the same thing to 30-something agents.

Now, oridinarily I might just go ahead and send it out regardless. However, this is no form letter-- it's been typed with my name, address, and the title of my novel. Is this just me or does that indicate a degree of seriousness?

Any advice appreciated.

Okay, I've decided to send it with the following text:

At your request, I am pleased to send you the first three chapters and a synopsis of my 96,300-word novel, [Title]. You had requested exclusivity; unfortunately, I have already sent out partial manuscripts to several other agents. Nevertheless, if you will be so kind as to take a look at my work, I will certainly keep you apprised of any developments with other agencies. Should you desire the full manuscript, it will of course be entirely exclusive.

DeadlyAccurate said:

I'd drop that last sentence. What if you get a full request first from another agency that doesn't insist on exclusivity?

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Then they'll just have to wait a bit. I'm totally fine with agents asking for an exclusive on a full manuscript. It seems logical to me; they don't want to waste their time when you may end up signing on with someone else. In any case this agency is quite reputable and I am willing to take the risk. Actually, I'm surprised they requested anything, as they are listed as "very exclusive" in the Guide to Literary Agents.

DeadlyAccurate said:

Then how about "Should you desire the full manuscript, I'll be happy to provide it on an exclusive basis if possible."

The "of course" forces you to live up to a promise that, through no fault of your own, you may not be able to.

ETA: A reason why exclusives suck for writers: it makes it nearly impossible for you to choose from among multiple agent offers.

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Let's just say this: If this agency wanted to represent me, I wouldn't care about shopping around. So I'm not sending any fulls out until I hear back from them (which will be soon judging on their super fast response to my query). Hence no moral dilemma with the inclusion of "of course." I actually mean what I say.