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I too like Rojo's answer. And Mr. Wizard's answer is intriguing as always. A third possibility is adding the condition that the Heads of second and third arguments are not Rule after the LHS. So, the following also works

 Options[f] = {"g" -> Identity};
 f[x_, y_: 2, z_: 3,  OptionsPattern[]] /; (Head[y] =!= Rule =!= Head[z]) := 
 OptionValue["g"][x + y + z]

The condition could be alternatively stated as OptionQ[y]=!=True=!=OptionQ[z].

I too like Rojo's answer. And Mr. Wizard's answer is intriguing as always. A third possibility is adding the condition that the Heads of second and third arguments are not Rule after the LHS. So, the following also works

 Options[f] = {"g" -> Identity};
 f[x_, y_: 2, z_: 3,  OptionsPattern[]] /; (Head[y] =!= Rule && Head[z] =!= Rule):= 
 OptionValue["g"][x + y + z]

The condition could be alternatively stated as (OptionQ[y] =!= True && OptionQ[z] =!= True).

I too like Rojo's answer. And Mr. Wizard's answer is intriguing as always. A third possibility is adding the condition that the Heads of second and third arguments are not Rule after the LHS. So, the following also works

 Options[f] = {"g" -> Identity};
 f[x_, y_: 2, z_: 3,  OptionsPattern[]] /; (Head[y] =!= Rule =!= Head[z]) := 
 OptionValue["g"][x + y + z]

I too like Rojo's answer. And Mr. Wizard's answer is intriguing as always. A third possibility is adding the condition that the Heads of second and third arguments are not Rule after the LHS. So, the following also works

 Options[f] = {"g" -> Identity};
 f[x_, y_: 2, z_: 3,  OptionsPattern[]] /; (Head[y] =!= Rule =!= Head[z]) := 
 OptionValue["g"][x + y + z]

The condition could be alternatively stated as OptionQ[y]=!=True=!=OptionQ[z].

Specifying the Head of the last argument instead of the first two optional arguments, the following also works

 Options[f] = {"g" -> Identity}; 
 f[x_, y_: 2, z_: 3, opts : OptionsPattern[]] := OptionValue["g"][x + y + z]

I too like Rojo's answer. And Mr. Wizard's answer is intriguing as always. A third possibility is adding the condition that the Heads of second and third arguments are not Rule after the LHS. So, the following also works

 Options[f] = {"g" -> Identity};
 f[x_, y_: 2, z_: 3,  OptionsPattern[]] /; (Head[y] =!= Rule =!= Head[z]) := 
 OptionValue["g"][x + y + z]