Of revealing or publicizing either substantially true

and

The intent is to make a gain (for themselves or anyone else) or cause a loss (to anyone),

and either
(a) The perpetrator did truly believe that the demand was based on reasonable grounds
or
(b) The perpetrator did truly believe that the menace was a proper way to reinforce the demand.
(or both)

The law considers a "demand with menaces" to always be "unwarranted" (unjustified), unless the perpetrator actually believed that his/her demand had reasonable grounds, and also actually believed that the menace was a proper way to reinforce that demand. These tests relate to the actual belief of the perpetrator, not the belief of an ordinary or reasonable person. Therefore, tests related to what a "reasonable" person might think, and tests of dishonesty, are not often relevant - the matter hinges upon the actual and honest beliefs and knowledge of the perpetrator him/herself. The wording of the Act means that there is a presumption in law that demands and/or menaces are likely to be deemed unwarranted, unless the perpetrator shows evidence that they were believed not to be.^[16] However, once a perpetrator has defended him/herself by giving evidence related to the demand and menace both being believed warranted, the prosecution must overturn one or both of these claims to prove their case. The usual rule is that a criminal act, or a belief not truly held, can never be "warranted", although according to some authors, a "grey area" may (rarely) exist where a very minor illegality may be honestly believed to be warranted.^[17]
Additionally, a statement that would not usually coerce or pressure someone may still be a "menace", if the perpetrator knew, believed, or expected that their specific victim would feel coerced or pressured by it. The law does not require a demand or menace to be received by the victim, merely that they are made, therefore it is irrelevant whether the victim was affected or not, or even unaware of them (perhaps because they had not yet been received, read or listened to). Because the criteria include an intention to "cause" some kind of gain or loss, a demand for sex (for example) would not be considered blackmail, so threats with these and other demands are dealt with under a variety of other criminal laws. However even in these cases, a gain or loss of some kind can often be found, and then this law can then be applied.
In some cases, the perpetrator him/herself may claim to have acted under duress. The courts have ruled that a person who places themselves in a situation where they may be coerced to make a demand with menaces against a third party is likely, foreseeable, or probable, may not be able to rely on coercion as a defence because they voluntarily placed themselves in such a situation. This issue has arisen, for example, in gang-related violence.^{[18][19][20][21]}
Menaces
The word "menaces" was adopted from sections 29(1)(i) and 30 of the Larceny Act 1916. Section 29(1)(i) made it a felony for a person to utter, knowing the contents thereof, any letter or writing demanding of any person with menaces, and without any reasonable or probable cause, any property or valuable thing. Section 30 made it an offence for a person to, with menaces or by force, demand of any person anything capable of being stolen with intent to steal the same.
Thorne v Motor Trade Association (1937)^[22] is a leading case on the meaning of the word "menaces", decided under section 29(1)(i) of the Larceny Act 1916.^[23] The issue to be decided was whether the statement by a powerful trade association that a person found guilty of breaking their rules on price fixing would be "blacklisted", but could avoid this fate by paying a fine, was a "menace". It was held that the trade body had both the right to put persons on their blacklist and also the right to offer a fine as an alternative to being put on a blacklist, therefore neither of the demand or the menace were ruled to be "unwarranted". (The Court noted that a plainly unreasonable fine could potentially be viewed as unwarranted.) In this case, Lord Wright said:
I think the word "menace" is to be liberally construed and not as limited to threats of violence but as including threats of any action detrimental to or unpleasant to the person addressed. It may also include a warning that in certain events such action is intended.^[24]
And Lord Atkin said:
The ordinary blackmailer normally threatens to do what he has a perfect right to do namely, communicate some compromising conduct to a person whose knowledge is likely to affect the person threatened. [...] What he has to justify is not the threat, but the demand of money.
The gravamen of the charge is the demand without reasonable or probable cause: and I cannot think that the mere fact that the threat is to do something that a person is entitled to do either causes the threat not to be a "menace" [...] or in itself provides a reasonable or probable cause for the demand.^[25]
R v Clear^[26] was decided under section 30 of the Larceny Act 1916. Sellers LJ said:^[27]
Words or conduct which would not intimidate or influence anyone to respond to the demand would not be menaces ... but threats and conduct of such a nature and such an extent that the mind of an ordinary person of normal stability and courage might be influenced or made apprehensive so as to accede unwilling to the demand would be sufficient for a jury's consideration.
and that:
There may be special circumstances unknown to the accused which would make the threats innocuous and unavailing for the accused's demand, but such circumstances would have no bearing on the accused's state of mind and of his intention. If an accused knew that what he threatened would have no effect on the victim it might be different.
In regard to the importance of the perpetrator's understanding of impact, in R. v Billy Joe (William) Temple (2008), the Court of Appeal reduced the perpetrator's original sentence because it did not take into account, among other things, the appellant's lack of appreciation of the extreme nature of the impact of the menace to which he had been a party.^[28]
In R v Lawrence and Pomroy,^[29] the defendant argued that the direction given to the jury should have contained a definition of the word "menaces" in accordance with R v Clear. Cairn L.J. said:
The word "menaces" is an ordinary English word which any jury can be expected to understand. In exceptional cases where because of special knowledge in special circumstances what would be a menace to an ordinary person is not a menace to the person to whom it is addressed, or where the converse may be true, it is no doubt necessary to spell out the meaning of the word.^[30]
In R v Lambert (2009), it was held that:
[A] demand does not have to be made in terms of a demand or requirement or obligation. It can be couched in terms which are by no means aggressive or forceful. Indeed, the more suave and gentle the request, the more sinister in the circumstances it might be.^[31]
The word "menaces" has been held to include the following:

• 
  a threat to publish attacks on a company calculated to lower the value of its shares^[32]
  
• 
  a threat to reveal that the victim has not honoured a debt^[33]
  
• 
  a threat to place the victim on a trade association's "stop-list"^[34] - although in that specific case, the menace was found not to be "unwarranted" because it was believed - and the court agreed - that it was justified and reasonable. The court commented that if the fine had been completely unreasonable, the menace might have become unwarranted as a result.
  
• 
  a threat to refrain from giving evidence in an action^[35]
  
• 
  words such as "I'm not threatening you. I'm giving you a promise. Let's just leave it at that", or "I've not sent nobody to see you yet" ^[36]
  
• 
  a person who phoned a relative posing as a victim of false imprisonment, to say he was at risk of harm and needed money to pay off his captors and be freed. In this unusual case, although posing as the victim and not threatening harm to the relative, the statement was capable of being a menace because of its coercive nature and the pressure it would apply on the victim, it was unwarranted, and there clearly was a demand. The ruling stated that "It is how the demand and menace affects the victim that matter".^[31]
  

Professor Griew said that the word "menaces" could conceivably include:^[23]

• 
  a threat of physical violence to the victim or another
  
• 
  a threat of prosecution
  
• 
  a threat to reveal actual criminal offending or sexual misbehaviour^[37] or to publish false allegations of the same
  

David Ormerod said that it extends to a threat to damage property.^[38]
It should be remembered that the offence requires either an unwarranted menace, or an unwarranted demand, or both; not all menaces nor all demands are "unwarranted", and the belief of the perpetrator is the determining factor. If both the demand and the menace are each believed to be proper and reasonable to make, in law, then - depending upon the details of the case - the kinds of actions listed above may no longer be criminal offences. However, as stated above, a criminal demand or menace can never believed to be "warranted", and actual knowledge of the victim and their state of mind or expected response may change a warranted matter into an unwarranted one.