If you create an accelerated/managed image, is an image you get returned from subimage() accelerated as well?
For example…
Image preImage =javax.imageio.ImageIO.read( getClass().getResource(path));
GraphicsConfiguration gc = window.getGraphicsConfiguration();
BufferedImage accelImage = gc.createCompatibleImage(
preImage.getWidth(null),
preImage.getHeight(null),
Transparency.BITMASK);
Graphics2D accelImageG = (Graphics2D) accelImage.getGraphics();
accelImageG.setComposite(AlphaComposite.Src);
accelImageG.drawImage(preImage, 0, 0, null);
accelImageG.dispose();
BufferedImage subimage = accelImage.getSubimage(0, 0, 32, 32)
Is the subimage accelerated/manged?
Thanks! 
