I don't have a Poodle but used to years ago. Tear staining can be brought on by a variety of reasons. Some say it's chemicals in the drinking water or the food they are eating. It could also be caused from allergies. The most common problem though for Poodles is the hair around the eye, specifically the eye lashes irritating the eye itself. Give your boy a close examination and watch when he blinks. If you suspect that the eye lashes or hair around the eyes may be the problem, take him to a professional groomer to have the hair trimmed. Of course this isn't a fix since the hair will grow back, but if there is a problem with the eyelids rolling inward that can be corrected. You could also wash the tears everyday with very warm water and see if the problem subsides a little. At any rate if you suspect any irritant to the eye itself, see your vet immediately. Any small scratches or damage to the eyes can bring on bigger problems in the future, up to and including glaucoma.
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Bob
If there are no dogs in Heaven, then when I die I want to go where they went.