"The earliest layer of the gospel tradition is made up of single aphorisms and parables ....."
The Five Gospels, R.W.Funk et al., p.28

Procedures for identifying the remaining logia sayings

My original procedure

In the page 'Pericopes wrongly assigned to Q' I argued that Luke took from Matthew some of the material usually allocated to Q. This included the following pericopes: Mt 3:7-12; 4:1-11; 8:5-13; 11:2-19; 20-23; 25-27; 12:22-32; 43-45; 22:1-10; 23:37-39; 24:45-51; 25:14-30.

By default, all the remaining double tradition material was deemed to be compatible with the template sayings and was therefore was assigned to the logia.

In addition to the four source doublet sayings not in the Double Tradition, there are several other non-doublet sayings which Q scholars do not normally assign to Q, but which I took as probably belonging to the logia:

The reasons for assigning each of these to the logia are explained individually here:
  A commentary on the sayings of Jesus.

My new new and more consistent procedure

This takes nothing by default, but requires positive evidence for a candidate logia saying before it is accepted as such.

Basic initial checks

For each candidate saying, we need first to make the following checks (which were not needed for the source doublets because the positive evidence for them ensured that they would have passed the checks):

Check for compatibility with the template

We should check that a candidate saying doesn't contradict any template saying.

The positive evidence needed for the remaining candidate sayings

Each must have at least one of the following three characteristics:

Semitic poetry

There are three main features which can indicate Semitic poetry: couplets, parallelism and chiasm. (There is some overlap between the first two of these features.)

Couplets

A couplet is a two-line piece of poetry which is usually meaningful without a context. The exceptions for New Testament sayings are contexts of mission or the end times, which are sometimes assumed. Examples are:

Can a blind person lead a blind person?
Will not both fall into a pit?

Every one who exalts himself will be humbled,
and he who humbles himself will be exalted.

Whoever welcomes you welcomes me,
and whoever welcomes me welcomes the one who sent me.

This last couplet assumes the context of a mission initiated by Jesus and carried out by his followers.

Parallelism

This occurs when two lines of poetry convey the same message in similar words (synthetic parallelism), or when they convey the opposite message (antithetic parallelism). Below are examples of each type.

There is nothing covered up that will not be uncovered,
nothing hidden that will not be made known.

He who finds his life will lose it,
and he who loses his life for my sake will find it.

Chiasm

A good example is the following:

Do not store up for yourselves treasure on earth,
  where moth and rust consume, and where thieves break in and steal;
    but store up for yourselves treasures in heaven,
  where neither moth nor rust consumes and where thieves do not break in and steaL.
For where your treasure is, there your heart will be also.

The first and fifth lines are about treasure. The second and fourth lines are about thieves. If there is an odd number of lines as in this case, the middle line usually sums up the message of the whole stanza.

Hyperbole

Primary example

The New Testament example which best illustrates this characteristic is the following:

It is easier for a camel to go through the eye of a needle
than for a rich man to enter the kingdom of God.

Many people have tried to remove the absurdity of this saying by arguing that the original words for "camel" or "eye of a needle" applied to some feature known to the local community, or that they must have been mistranslated. However in this example Mark wrote that the action in the first line is "impossible" (Mk 10:27). Therefore at the time his gospel was written, the saying was already understood as absurd, i.e. as hyperbole, and there is no reason to think that the original version of the saying was any different in this respect.

Other examples