CMYK to CMYK conversion Dmax warning

Found an error in the way Photoshop converts from one CMYK profile to another CMYK profile....
When converting from RGB or LAB to CMYK, photoshop will follow the Dmax settings of the CMYK profile you are converting to.  However, if you convert from a CMYK file with a high Dmax to another CMYK profile with a lower Dmax setting, your new file will NOT have the lower Dmax.
For example, If I convert a CMYK file with a 340 Dmax to a CMYK profile with a 300 Dmax, the colors will shift but the new file will have a Dmax of 340, NOT 300.
The only solution to this is to convert from CMYK to LAB, then back to your new CMYK profile.  Then photoshop will use the correct Dmax settings.
I know you shouldn't convert from CMYK to CMYK, etc etc.  But sometimes it isn't avoidable for various workflow reasons.  And I understand why photoshop is unable to convert to the new Dmax when you're going from CMYK to CMYK.  But, I feel that this is such a critical color issue that photoshop should warn you that to get a propper Dmax, you can't go from CMYK to CMYK.
It seems that anyone who is working with CMYK should be extremely concerned about Dmax, so for Photoshop to not warn you about this issue is to invite serious color problems which may not be caught until you're going to press... which is a very stressful time to make such discoveries.
Thanks!!!

Chris-
I figured out what is going on... we're both right.  Photoshop does properly change the CMYK profile and dmax when you are converting to a new profile, IF the file you are converting from has an embedded profile.
However, it is fairly common in closed CMYK workflows to not embed the icc profile due to conflicts with other parts of the process.  When you try to convert an image that does not have an embeded profile, Photoshop assumes the "mystery" image has the working CMYK profile.
Since the assumed profile, and the destination profile were the same, it did no conversion  (or merely assigned the profile) even though you had selected "Convert to ...."
This resulted in images which were outside the Dmax of the CMYK profile we had converted to....because it didn't actually convert.
There are 3 ways around this.
(1) You can include the embeded profile, and Photoshop will do the propper conversion.
(2) You can Change your working CMYK profile to the profile of the image you are converting, and photoshop will assume (correctly) that it is the working profile.
(3) You can convert the image to LAB or RGB and then to the desired CMYK profile, however this will only work properly if you tell photoshop which profile you are starting from... otherwise it may assume the incorrect profile.  This will end up with an image which conforms to the desired color space, however you may get extremely undesirable color shifts due to the incorrect assumptions about the initial color space.
So, the question becomes, is this a case where Photoshop should protect the user from themselves?  Should photoshop be checking when it converts an image with no embeded profile to make sure the resulting file conforms to the destination color space?  It sort of does with the profile warning dialogs which are turned on by default... but everyone I know turns those off as soon as they start using photoshop. 
Does this happen in RGB too?  For example, if my working RGB profile is sRBG, is photoshop going to assume an unknown color profile to be sRGB?  So when I output for web use, is it actually converting an unknown color profile to sRGB, or is it merely assigning like it does with CMYK?
I'm pretty sure this is what's going on, let me know if I've made any mistakes in my assumptions.
Thanks!
-Mark

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