Hi,
Well done for adjusting your diet and cutting out the worse elements .You have already cut your Hb A1c by doing so, but the damage done earlier may take some time to alleviate. Sadly some people do get complications at lower levels than others.
You don't say anything about what you've done with your insulin regime. I think that for many people it is possible , using modern insulins, to eat a diet containing a reasonable number of good quality carbohydrates,(much as you are now doing) and to achieve HbA1cs within normal ranges. I do, so I'm going to give different suggestions to Fergus. As the titles of the books say you need to learn to 'Think like a Pancreas' and 'Use Insulin' rather than just dose with it.
(There are 2 excellent books that are invaluable: Garry Scheiner Think like a Pancreas and John Walsh, Using Insulin.)
Your basal insulin needs to be correct, your carb to insulin ratio needs to be correct and you need to have some idea of the effects of individual meals on your BS. For example most people find that because meals high in fat (and sometimes protein) or lower in glycemic index take longer to 'digest' and sometimes have to split their bolus insulin over 2 injections to cover them effectively. Some people find some carbs have far greater effects on their own metabolism than others. You also need fairly good carb counting skills.
From your figures I assume that you're going to bed with a reading of 8.7 and waking up at 5.8mmol.
This may be because you are not using a high enough insulin/carb ratio for your evening meal and are going to bed with a high BS. If so your basal is then dropping your BS. Basal insulin is meant to keep your BG stable, not to reduce it .
The readings that you don't give are the 2 hour post prandials. How high are you at 2 hours?, It may in fact be that you are going relatively high after each meal and that you are relying on your basal to reduce the BS to the premeal figure. In that case the basal may be too high and all the boluses too low . Testing should help you find out.
Different people have different profiles through the day, I take less insulin to carb for breakfast and more for the evening meal but others have an opposite profile.
A possible first action is to test your basal dose, you can do this by missing a meal and testing, your BG should not rise or fall significantly. This article, from an American forum, tells you how to go about it
http://www.diabetesdaily.com/forum/articles/16675-basal-testing-multiple-daily-injections Some people find it is better to split levemir, half in the morning and half at night.
Once your basal is correct you should not have to fear unexpected hypos (though you will have to account for extra exercise) You can then start to adjust your bolus rates. If for some reason you find that you can't achieve this, perhaps because of a very varied lifestyle or a very uncoperative liver, then it may be a good idea to investigate using an insulin pump which would allow you to adjust more minutely.