The guidelines in the History Short Essay Rubric are only the essentials
and provide the minimum of what a History essay should be. Beyond the
basics of establishing a thesis and then forming arguments and evidence in
support of it, those who evaluate History papers - Professors, Teaching
Assistants, and readers - will be looking for more.  What they will be
looking for is summed up in the points below.

Fulfillment of Assignment:  The best place to start is to be sure that you
are doing what the assignment calls for.  If a particular question or
subject is assigned, be sure that your thesis addresses it in some direct
way.  If certain sources are at the core of the assignment, be sure they
are at the core of your paper.  If you are called on to write a specific
type of essay, be sure that you do.  If unsure, ask. 

Grasp of Sources:  Remember that there is a purpose to writing
assignments:  your instructors want to be sure that you understand what
they are teaching.  Be sure you know and understand the material.  No
amount of literary virtuosity can save you if you do not know what you are
talking about.  You should be sure to read and use the en tire source, and
not just one section of it.  You should also be sure that your
interpretation is historically appropriate.  A perfectly reasonable
twentieth-century literary or political understanding of something may
make no sense at all in the Ancient Mediterranean or eighteenth-century
China.  Be true to the period and the culture involved. 

Quality of Argument:  A firm understanding of a source in its context,
well-selected evidence, and an incisive thesis are the basic necessities. 
However, the manner in which they are presented will determine one's
success.  Well-constructed arguments flow logically from one to the other,
not leaving the reader to figure out how they rela te.  And evidence
should be used with brevity.  The right quote can bring the spirit of a
period to your argument, but only if it is apt to your subject and
phrasing.  Otherwise, paraphrase succinctly, using enough detail to be
clear, without overwhelming your point with needless story-telling.

Persuasiveness:  Ultimately, the quality of an essay is measured by
whether or not the reader is persuaded by the thesis.  Let this guide you
while you write, and when you are deciding whether or not you have made
your point sufficiently.