1 After the more frequent, more basic verbs such as say, think, and notice, the word that is often left out, especially in speech.
I said there was to be no talk of divorce.
I think he made a tactical blunder by announcing it so far ahead of time.
However, that tends to be used when the that-clause is separated from the Subject by a prepositional phrase, adverb group, or subordinate clause.
A Foreign Ministry spokesman said at a press briefing that relations with the Community were strained.
That is less often left out after more formal or less frequent words such as demand, estimate, and brag, and is retained when the rhythm of the sentence requires it.
...the legendary pianist, composer and band leader who bragged that he had invented jazz.
They demanded that he step down immediately.
4 In the case of meaning groups 1-5, the Subject and verb can, as with a quote clause, come within or after the that-clause, without the word that, unless the verb expresses a statement or request that something should be done.
Things didn't, he admitted, look good in Russia.
The 19-year-old player is not thought to be happy with the terms offered to him. Negotiations were continuing, he confirmed.
5 Some of the more frequent verbs concerned with speech, writing, and thought are also used in clauses beginning with as, which usually come before or within a main clause without that. This structure implies that, in the opinion of the user, what was said or thought is true, or turned out to be true.
As the author says, a food diary is really useful in finding out the cause of food-related allergies.
He had, as he predicted, immediately assumed an non-executive chairmanship.
6 Some of these verbs can be used in a clause beginning with as or than when making a comparison between what people say or think about a situation and what it is really like.Some verbs that have the pattern V that also have the pattern V so or V so/not, where so or not acts as a substitute for a that-clause. See Section 14 below.
I'm not as disheartened as people think.
When the doorbell rang, Marianne thought it might be Jake arriving earlier than he had promised.