I call glTexImage2D with a parameter level = 0. Then I call glGenerateMipmap(GL_TEXTURE_2D). What happens with GL_TEXTURE_BASE_LEVEL and GL_TEXTURE_MAX_LEVEL ? I assume that they are automatically set this way:

Code :
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_BASE_LEVEL, 0);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAX_LEVEL, mipmapsCount - 1);

Later I can set above parameters manually and for example reduce the max level. Is that right ?