The authority came under fire after collections were suspended on Wednesday and Thursday after 'Beast from the East' blizzards brought parts of the town to a standstill.
But the authority has said there will be no reduction or refund of Council Tax over missed collections and has issued a lengthy statement on how it plans to catch up with the backlog caused by last week's disruption.
A statement on the council's website said: "We understand there is a lot of anger from people about bins following last week’s bad weather.
"The council and Suez have thought very carefully about what we should do – our decision has not been made through laziness or lack of planning – there are so many different things to balance.
"The disruption couldn’t have come at a worse time, right before the start of the new waste and recycling service.
"It is absolutely vital that people know what bin they’re putting out on what days so for us to change this now, on the very week when the new collections are due to begin, we’d risk causing even more confusion for people.
DMBC posted a new calendar to every resident last month, and the authority says doing an extra black collection for some residents and not others would make the calendars wrong.
The statement added: "It would mean that people didn’t know what bin was due for collection next week and the week after, some people would have two consecutive black collections and others wouldn’t, and Suez would have to find a lot of extra resource from elsewhere to be able to do it. All round, it would be a nightmare.
"Doing that would impact almost every resident, and lead to even more confusion and anger than we currently have. While we don’t have any ideal scenario, we’ve picked the approach which is going to create the least amount of problems for the fewest people."
Here's what's happening:
* Your new collection dates will stay exactly the same as what is on your calendar, to avoid confusion. You can also view your collection dates online.
"We know this means that some of you will go up to 3-4 weeks without a black bin collection, and we’re really sorry about that. Unfortunately though, the only other options will cause way too much confusion and will be negative for everyone.
"Suez have confirmed that, if your bin was missed last week because of the snow, the collection teams will take a reasonable amount of rubbish if it is bagged up and put next to your black bin on your next black bin collection day.
"We know some of you will have a lot of extra rubbish, so we understand you might need to put a few extra bags out. This side waste may be collected by a separate bin lorry so please don’t worry if it’s not taken at the same time as your black bin is emptied.
"We know it’s really difficult to keep rubbish in loose black bags until your next collection – if you can take it to a Household Waste Recycling Centre, then please do. If you can’t get to a HWRC though, our advice is to double-bag any extra waste, make sure it’s tied up securely and store it in a secure place like a shed or a garage. If you don’t have a shed or a garage, then store extra bags in a suitable container, like your green/blue bin, and remember to take it out before your next collection.
"Like the black bins, please check your new calendar for the date of your recycling collections (blue and green bins) and any recycling that wasn’t collected last week will be taken then.
"You’ll need to put any glass into a separate green box - if you have too much recycling for your blue bin, then you can put this out in your old green boxes or in small bags next to the blue bin and the collectors will take it all. Just please make sure glass is kept separate from everything else.
"It’s really annoying when a key service hasn’t been provided, for whatever reason. We know that – we’re local people with bins too.
"However, council tax doesn’t just get spent on bin collections – in last week’s bad weather we had members of staff working around the clock to treat the roads, visit vulnerable residents at home and keep all our vital services running. Waste collectors did try to keep working for as long as possible and only stopped when it wasn’t safe anymore. We’ve also really carefully considered how to catch up with the collections and tried to minimise the impact on local people."