After buying and returning several sponge mops from homeowner stores and Smart & Final, etc. because they just did not do the job, I have struck pay dirt.
At a professional cleaning supply house, I bought a sturdy mop made of REAL sponge, with a strong wringer. The saleslady said it should last 10 years. It cost about $24.00, but if it performs as represented, will be well worth it.
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