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I've used a lot of online wallets: xapo, wirex, cryptopay, blockchain, etc. But recently these wallets have started to disappoint with their fees (xapo), transaction time (blockchain), rates (wirex) and complex verification. So I was wondering are there any new good wallets with reasonable fees and their own debit cards?
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No. Basically no web wallet provides the level of control that many desktop wallets provide (e.g. coin control, fee control). Many of them are just exchanges and are custodial wallets so you don't really control the Bitcoin since you don't control the private keys.
I highly recommend that you avoid using web wallets as much as possible. If you do choose to use a web wallet, use one that is listed on bitcoin.org as those wallets have to meet certain criteria before being listed.
Thanks for participating to Bitcoin.SE, however please note that this question is off-topic as per the [help/on-topic] for being a software request. Off-topic questions can be closed and deleted, which would nullify your contribution! You can flag such questions for closure with the "flag" button. – Kyll – 2017-06-15T18:51:35.317