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New ICC profiles for AIJP papers are currently in progress and will be available here in September. Profiles for KOZO THIN/THICK WHITE (aka 'MOENKOPI KOZO') and UNRYU (aka 'MOENKOPI UNRYU') may be found here: 
https://www.moabpaper.com/icc-profiles-downloads/
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Additionally, custom ICC profiles may be ordered through our US distributor, 'Freestyle Photographic' here: 
https://www.freestylephoto.biz/15076-Freestyle-Custom-Printer-Profile
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Note from Freestyle Photographic:
"For Awagami AIJP papers, select 'Epson Velvet Fine Art' for the media setting and the profile in your print driver. We then recommend selecting "Photoshop Manages Colors".  
Additionally, under "Rendering Intent", we recommend selecting "perceptual" with "black point compensation" checked.  
Finally, because AIJP papers tend to render a bit flat, Eric Joseph an authority on Inkjet printing, suggests using the "Velvet Fine Art" profile setting you have in the printer driver and also upping Saturation & Contrast a bit to punch the color.”