How astute! It's great for you to want to know how to help your dog's oral care better.
1) use only VOHC (Veterinary Oral Health Care) approved products. These products go through a rigorous approval process. Greenies are VOHC approved. All CET brand products are approved. My dog prefers CET Veggie Dents.
There are other home care options more than chewing that can help prevent tartar. A combination of A) prescription dental diets, B) VOHC approved chewing products, C)dental rinses, and D) brushing daily or oravet sealant weekly (easier for my life - I can't find the time to brush my dog's teeth every day, but I can put the sealant on each week in 1 minute a week) is the best approach to dental home care.
Please be advised that no home care can take away the tartar that is already present. The tartar present harbors bacteria that microscopically daily get into the bloodstream and shower to other organs particularly the kidneys and heart. Please have your dog's teeth cleaned at least yearly under anesthesia to prevent internal organ damage and try to prevent tooth loss.
Small dogs like your miniature poodle and my miniature dachshund are quite prone to poor oral health and the subsequent problems they cause. Regular dental care will add an average of 2 years of quality life to your little guy.
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