Since what really makes or breaks my flemish 16th c costume is the headwear I decided to make a special page with documentation on the different types seen in paintings of middle class or upper class people from the second part of the 16th century. Although the "hats", for lack of a better word I will call them hats, are basically the same, you can actually make a distinction between two types, based on the shape of the coif worn under the veil.
The first type is made of two parts, one part that fits the head closely and a probably circular piece of fabric attached to it.

	Anthonis Mor: Portrait of a Lady,1555-1560 The under cap, or coif seems to be made mostly of lace.The front piece is probably wired to keep it's shape and you can't see any visible gathers on the back part. It also seems to be mor "puffy" in top than on the sides and back.
	Frans Pourbus the Elder, 1545-1581: Portrait of a woman Here you see the gathers more clearly. The entire cap seems to be made of a sheer material or lace.
	Frans Pourbus the Elder, 1545-1581: Portrait of a lady I argued with myself whether this was the same type of cap or if it should go with the straighter, one piece type below, but after looking at it real closely I think I can see a rounded part far back on the head.
	Cournelius de Zeeuw (attributed): Pierre de Moucheron and his wife, Isabeau de Berbier with their children in Antwerp, 1563 If you look at the young girls who are the only women not wearing black, you can see that they are wearing the same type of coif or caul as the older women, but made of red and gold instead of white. There doesn't seem to be much gathering, so I guess that the diameter of the circle is pretty small.

Conclusion: I think this is a two part cap with a flat, quite stiff, front part which is probably wired. It is usually decorated with lace. The other part is a gathered circle of fabric. It's probably attached unevenly, so that the most of the gathers are on top of the cap.The circle can not be very big and the gathers must be really small, since they are hard to see in most paintings. To keep it rounded there might be a roll of some material, like wool or wool felt attached under it, but the fact that the cap is often made of lace or some other sheer material suggests otherwise. Instead, the cap probably got it's shape with the help of starch.

Courtesy of La Couturière Parisienne	Frans Pourbus the Elder, 1545-1581: Woman with white hood Note the straighter shape of the cap. There also appear to be some blackwork along the edge.
	Catherina van Hermessen: Self portrait, 1548 The same combination of a straight cap and veil as above. These caps seem to be set further back than the type above.
	Ambrosius Benson, ca 1495-1550: Portrait de jeune femme à la bague In this earlier image you can see a very similar headwear, although the veil isn't wired. It's shape and body caused by the fabric being stiff, either on it's own or with the help of starching.

All these portraits are made by flemish painters and I think it's safe to say that this was a fashion that was typical for Flanders, or at least the Low Countries in the second half of the 16th century in Flanders.
The white headwear combined with the almost uniformmaly black dresses gives a sober impression and in a way points forward to the dutch fashions of the 17th century