Synonyms : centrist, middle of the roader, moderationist

Example : Moderate prices.
A moderate income.
A moderate fine.
Moderate demands.
A moderate estimate.
A moderate eater.
Moderate success.
A kitchen of moderate size.
The X-ray showed moderate enlargement of the heart.

Example : A moderate penalty.
Temperate in his response to criticism.

Synonyms : temperate

Example : Moderate in his demands.
Restrained in his response.

Synonyms : restrained

Example : John moderated the discussion.

Synonyms : chair, lead

Example : Moderate your speed.

Example : Moderate your alcohol intake.
Hold your tongue.
Hold your temper.
Control your anger.

Synonyms : check, contain, control, curb, hold, hold in

Example : He moderated his tone when the students burst out in tears.

Synonyms : mince, soften

Example : Tone down that aggressive letter.
The author finally tamed some of his potentially offensive statements.

Synonyms : tame, tone down

Example : She tempered her criticism.

Synonyms : mollify, season, temper