dealing with not quite lognormal data

[magoo2]

I am dealing with some data that is skewed. The median is lower than the mean and the standard deviation is fairly high. The outliers have a significant influence on the mean and the standard deviation. When I do a natural log or ln transformation, it looks somewhat but not quite normal. I'm trying to find out what amount of inaccuracy I'm getting if I blindly proceed along the lines that it is a lognormal distribution.

I looked at the normality test in MiniTab and it looks like an arc or a boomerang shape rather than a straight line. On the descriptive statistics of the ln data, I get a p value < .05, so it again confirms that the transformed data is not behaving like a normal distribution.

Any suggestions? I can post some of the data or results so far if that would help.

Thanks in advance.