I’ve got a short piece on 遠慮 over at Néojaponisme. It’s a rewritten version of one of my first posts – “How to Say No by Saying Yes”. Don’t forget that you can also make use of お断り as a “Hell no” for comedic purposes.
遠慮 is a useful phrase for avoiding ない, but かねます is a far more blatant dodge. It is a verb ending that attaches to the stem (most often to the verbs できる, する, 致す, and 負う) and means “can’t” or, more appropriately in this case, “unable to”.
So rather than use できない or できません, you can say できかねます which has the same fundamental meaning. This is, as you can probably imagine, an incredibly polite, serious way to say something. Personally I find it hilarious that you can just replace the unpleasant negative ending with one that isn’t negative and make it all better. I’d like to meet the first guy who did that.
(Oda Nobunaga: おい、お前。パイ作ってきてくれ。
Sound of head falling on tatami.)
In every case, the speaker finds him/herself unable to do something that puts him/her in an unfortunate position. かねます almost has a built in “unfortunately” along the same lines as 〜てしまった as well as a “we ask for your understanding” as in ご了承ください.
An extremely useful set phrase I learned in college is わたくしどもでは決めかねます, which can be used if you’re ever put on the spot to make a decision that is outside of your immediate jurisdiction; it literally means “I alone am unable to make that decision”, but it also sort of implies that you will consult your superiors.
する, 致す, and できる are generally attached to other verbs. For example, 賛成 (さんせい) – そういう考えもあるかもしれませんが、賛成できかねます。 “You may think that, but I (unfortunately) am unable to agree.”
負う, as ALC tells us, is often used to duck responsibility – 責任を負いかねます.
Very much like 遠慮, かねます is one of those secret code words/patterns that is able to convey a lot of meaning efficiently because everyone knows what it really means. You, too, can tap into all the trappings of かねます, as long as you know when you need to use them.