diff --git a/jws/options.go b/jws/options.go
index 9eb04e837..4509efa08 100644
--- a/jws/options.go
+++ b/jws/options.go
@@ -64,7 +64,7 @@ func (w *withKey) Protected(v Headers) Headers {
 // You will have to use a separate, more explicit option to allow the use of "none"
 // algorithm.
 //
-// The algorithm specified in the `alg` parameter must be able to support
+// The algorithm specified in the `alg` parameter MUST be able to support
 // the type of key you provided, otherwise an error is returned.
 //
 // Any of the followin is accepted for the `key` parameter:
@@ -117,11 +117,23 @@ func WithKey(alg jwa.KeyAlgorithm, key interface{}, options ...WithKeySuboption)
 
 // WithKeySet specifies a JWKS (jwk.Set) to use for verification.
 //
-// By default both `alg` and `kid` fields in the JWS _and_ the
-// key must match for a key in the JWKS to be considered to be used.
+// Because a JWKS can contain multiple keys and this library cannot tell
+// which one of the keys should be used for verification, we by default
+// require that both `alg` and `kid` fields in the JWS _and_ the
+// key match before a key is considered to be used.
 //
-// The behavior can be tweaked by using the `jws.WithKeySetSuboption`
-// suboption types.
+// There are ways to override this behavior, but they must be explicitly
+// specified by the caller.
+//
+// To work with keys/JWS messages not having a `kid` field, you may specify
+// the suboption `WithKeySetRequired` via `jws.WithKeySetSuboption(jws.WithKeySetRequireKid(false))`.
+// This will allow the library to proceed without having to match the `kid` field.
+//
+// However, it will still check if the `alg` fields in the JWS message and the key(s)
+// match. If you must work with JWS messages that do not have an `alg` field,
+// you will need to use `jws.WithKeySetSuboption(jws.WithInferAlgorithm(true))`.
+//
+// See the documentation for `WithInferAlgorithm()` for more details.
 func WithKeySet(set jwk.Set, options ...WithKeySetSuboption) VerifyOption {
 	requireKid := true
 	var useDefault, inferAlgorithm, multipleKeysPerKeyID bool
diff --git a/jws/options.yaml b/jws/options.yaml
index 5e1b5b2ad..f07d66d48 100644
--- a/jws/options.yaml
+++ b/jws/options.yaml
@@ -95,9 +95,14 @@ options:
       WithInferAlgorithmFromKey specifies whether the JWS signing algorithm name
       should be inferred by looking at the provided key, in case the JWS
       message or the key does not have a proper `alg` header.
-      
+
+      When this option is set to true, a list of algorithm(s) that is compatible
+      with the key type will be enumerated, and _ALL_ of them will be tried
+      against the key/message pair. If any of them succeeds, the verification
+      will be considered successful.
+
       Compared to providing explicit `alg` from the key this is slower, and 
-      verification may fail to verify if some how our heuristics are wrong
+      verification may fail to verify if somehow our heuristics are wrong
       or outdated.
       
       Also, automatic detection of signature verification methods are always
diff --git a/jws/options_gen.go b/jws/options_gen.go
index 3a7df7e4e..17f993927 100644
--- a/jws/options_gen.go
+++ b/jws/options_gen.go
@@ -235,8 +235,13 @@ func WithFS(v fs.FS) ReadFileOption {
 // should be inferred by looking at the provided key, in case the JWS
 // message or the key does not have a proper `alg` header.
 //
+// When this option is set to true, a list of algorithm(s) that is compatible
+// with the key type will be enumerated, and _ALL_ of them will be tried
+// against the key/message pair. If any of them succeeds, the verification
+// will be considered successful.
+//
 // Compared to providing explicit `alg` from the key this is slower, and
-// verification may fail to verify if some how our heuristics are wrong
+// verification may fail to verify if somehow our heuristics are wrong
 // or outdated.
 //
 // Also, automatic detection of signature verification methods are always