Hi Neil,
Larry's suggestion can help as long as the breeze stays relatively light, and you're not lying to any current... As soon as the breeze begins to come up, however, the load on your rode will increase rapidly, and it's not a good solution in a blow...
Do you have a secondary anchor on the bow? My boat can sail a fair bit at anchor when the breeze pipes up, and if it starts to bother me, I'll simply 'dangle' my second anchor - a 33 lb Bruce on 30' of chain - maybe just enough to rest on the bottom, depending upon the depth... Even in deeper water, if it's just hanging and not touching the bottom, the effect in reducing the amount of sailing can be pretty impressive...
best regards,
Jon