diff --git a/CHANGELOG.adoc b/CHANGELOG.adoc
index 67900b84..a859ad4c 100644
--- a/CHANGELOG.adoc
+++ b/CHANGELOG.adoc
@@ -15,6 +15,8 @@
 
 https://github.com/oxidecomputer/dropshot/compare/v0.16.5\...HEAD[Full list of commits]
 
+* https://github.com/oxidecomputer/dropshot/pull/1490[#1490] Added `map` and `try_map` to `Query`, `Path`, `Header`, `HttpResponseOk`, `HttpResponseCreated`, `HttpResponseAccepted`, and `HttpResponseHeaders`, similar to `map` and `try_map` that already exist on `TypedBody`.
+
 == 0.16.5 (released 2025-11-20)
 
 https://github.com/oxidecomputer/dropshot/compare/v0.16.4\...v0.16.5[Full list of commits]
diff --git a/dropshot/src/extractor/body.rs b/dropshot/src/extractor/body.rs
index 0c239baa..4bbdec18 100644
--- a/dropshot/src/extractor/body.rs
+++ b/dropshot/src/extractor/body.rs
@@ -51,7 +51,7 @@ impl<BodyType: JsonSchema + DeserializeOwned + Send + Sync>
     pub fn map<T, F>(self, f: F) -> TypedBody<T>
     where
         T: JsonSchema + DeserializeOwned + Send + Sync,
-        F: Fn(BodyType) -> T,
+        F: FnOnce(BodyType) -> T,
     {
         TypedBody { inner: f(self.inner) }
     }
@@ -60,7 +60,7 @@ impl<BodyType: JsonSchema + DeserializeOwned + Send + Sync>
     pub fn try_map<T, E, F>(self, f: F) -> Result<TypedBody<T>, E>
     where
         T: JsonSchema + DeserializeOwned + Send + Sync,
-        F: Fn(BodyType) -> Result<T, E>,
+        F: FnOnce(BodyType) -> Result<T, E>,
     {
         Ok(TypedBody { inner: f(self.inner)? })
     }
diff --git a/dropshot/src/extractor/header.rs b/dropshot/src/extractor/header.rs
index 644db013..317b8dbb 100644
--- a/dropshot/src/extractor/header.rs
+++ b/dropshot/src/extractor/header.rs
@@ -43,6 +43,26 @@ impl<HeaderType: DeserializeOwned + JsonSchema + Send + Sync>
     pub fn into_inner(self) -> HeaderType {
         self.inner
     }
+
+    /// Convert this `Header` into one with a different type parameter; this
+    /// may be useful when multiple, related endpoints take header parameters
+    /// that are similar and convertible into a common type.
+    pub fn map<T, F>(self, f: F) -> Header<T>
+    where
+        T: DeserializeOwned + JsonSchema + Send + Sync,
+        F: FnOnce(HeaderType) -> T,
+    {
+        Header { inner: f(self.inner) }
+    }
+
+    /// Similar to [`Header::map`] but with support for fallibility.
+    pub fn try_map<T, E, F>(self, f: F) -> Result<Header<T>, E>
+    where
+        T: DeserializeOwned + JsonSchema + Send + Sync,
+        F: FnOnce(HeaderType) -> Result<T, E>,
+    {
+        Ok(Header { inner: f(self.inner)? })
+    }
 }
 
 /// Given an HTTP request, pull out the headers and attempt to deserialize
diff --git a/dropshot/src/extractor/path.rs b/dropshot/src/extractor/path.rs
index 362eb7ae..ac4ab128 100644
--- a/dropshot/src/extractor/path.rs
+++ b/dropshot/src/extractor/path.rs
@@ -31,6 +31,26 @@ impl<PathType: JsonSchema + Send + Sync> Path<PathType> {
     pub fn into_inner(self) -> PathType {
         self.inner
     }
+
+    /// Convert this `Path` into one with a different type parameter; this
+    /// may be useful when multiple, related endpoints take path parameters that
+    /// are similar and convertible into a common type.
+    pub fn map<T, F>(self, f: F) -> Path<T>
+    where
+        T: JsonSchema + Send + Sync,
+        F: FnOnce(PathType) -> T,
+    {
+        Path { inner: f(self.inner) }
+    }
+
+    /// Similar to [`Path::map`] but with support for fallibility.
+    pub fn try_map<T, E, F>(self, f: F) -> Result<Path<T>, E>
+    where
+        T: JsonSchema + Send + Sync,
+        F: FnOnce(PathType) -> Result<T, E>,
+    {
+        Ok(Path { inner: f(self.inner)? })
+    }
 }
 
 // The `SharedExtractor` implementation for Path<PathType> describes how to
diff --git a/dropshot/src/extractor/query.rs b/dropshot/src/extractor/query.rs
index 8209a139..fa936c95 100644
--- a/dropshot/src/extractor/query.rs
+++ b/dropshot/src/extractor/query.rs
@@ -31,6 +31,26 @@ impl<QueryType: DeserializeOwned + JsonSchema + Send + Sync> Query<QueryType> {
     pub fn into_inner(self) -> QueryType {
         self.inner
     }
+
+    /// Convert this `Query` into one with a different type parameter; this
+    /// may be useful when multiple, related endpoints take query parameters
+    /// that are similar and convertible into a common type.
+    pub fn map<T, F>(self, f: F) -> Query<T>
+    where
+        T: DeserializeOwned + JsonSchema + Send + Sync,
+        F: FnOnce(QueryType) -> T,
+    {
+        Query { inner: f(self.inner) }
+    }
+
+    /// Similar to [`Query::map`] but with support for fallibility.
+    pub fn try_map<T, E, F>(self, f: F) -> Result<Query<T>, E>
+    where
+        T: DeserializeOwned + JsonSchema + Send + Sync,
+        F: FnOnce(QueryType) -> Result<T, E>,
+    {
+        Ok(Query { inner: f(self.inner)? })
+    }
 }
 
 /// Given an HTTP request, pull out the query string and attempt to deserialize
diff --git a/dropshot/src/handler.rs b/dropshot/src/handler.rs
index c978a4fd..539d912e 100644
--- a/dropshot/src/handler.rs
+++ b/dropshot/src/handler.rs
@@ -1077,6 +1077,30 @@ where
 pub struct HttpResponseCreated<T: HttpResponseContent + Send + Sync + 'static>(
     pub T,
 );
+
+impl<T: HttpResponseContent + Send + Sync + 'static> HttpResponseCreated<T> {
+    /// Convert this response into one with a different type parameter; this
+    /// may be useful when multiple, related endpoints return similar response
+    /// types that are convertible into a common type.
+    pub fn map<U, F>(self, f: F) -> HttpResponseCreated<U>
+    where
+        U: HttpResponseContent + Send + Sync + 'static,
+        F: FnOnce(T) -> U,
+    {
+        HttpResponseCreated(f(self.0))
+    }
+
+    /// Similar to [`HttpResponseCreated::map`] but with support for
+    /// fallibility.
+    pub fn try_map<U, E, F>(self, f: F) -> Result<HttpResponseCreated<U>, E>
+    where
+        U: HttpResponseContent + Send + Sync + 'static,
+        F: FnOnce(T) -> Result<U, E>,
+    {
+        Ok(HttpResponseCreated(f(self.0)?))
+    }
+}
+
 impl<T: HttpResponseContent + Send + Sync + 'static> HttpCodedResponse
     for HttpResponseCreated<T>
 {
@@ -1099,6 +1123,30 @@ impl<T: HttpResponseContent + Send + Sync + 'static>
 pub struct HttpResponseAccepted<T: HttpResponseContent + Send + Sync + 'static>(
     pub T,
 );
+
+impl<T: HttpResponseContent + Send + Sync + 'static> HttpResponseAccepted<T> {
+    /// Convert this response into one with a different type parameter; this
+    /// may be useful when multiple, related endpoints return similar response
+    /// types that are convertible into a common type.
+    pub fn map<U, F>(self, f: F) -> HttpResponseAccepted<U>
+    where
+        U: HttpResponseContent + Send + Sync + 'static,
+        F: FnOnce(T) -> U,
+    {
+        HttpResponseAccepted(f(self.0))
+    }
+
+    /// Similar to [`HttpResponseAccepted::map`] but with support for
+    /// fallibility.
+    pub fn try_map<U, E, F>(self, f: F) -> Result<HttpResponseAccepted<U>, E>
+    where
+        U: HttpResponseContent + Send + Sync + 'static,
+        F: FnOnce(T) -> Result<U, E>,
+    {
+        Ok(HttpResponseAccepted(f(self.0)?))
+    }
+}
+
 impl<T: HttpResponseContent + Send + Sync + 'static> HttpCodedResponse
     for HttpResponseAccepted<T>
 {
@@ -1120,6 +1168,29 @@ impl<T: HttpResponseContent + Send + Sync + 'static>
 pub struct HttpResponseOk<T: HttpResponseContent + Send + Sync + 'static>(
     pub T,
 );
+
+impl<T: HttpResponseContent + Send + Sync + 'static> HttpResponseOk<T> {
+    /// Convert this response into one with a different type parameter; this
+    /// may be useful when multiple, related endpoints return similar response
+    /// types that are convertible into a common type.
+    pub fn map<U, F>(self, f: F) -> HttpResponseOk<U>
+    where
+        U: HttpResponseContent + Send + Sync + 'static,
+        F: FnOnce(T) -> U,
+    {
+        HttpResponseOk(f(self.0))
+    }
+
+    /// Similar to [`HttpResponseOk::map`] but with support for fallibility.
+    pub fn try_map<U, E, F>(self, f: F) -> Result<HttpResponseOk<U>, E>
+    where
+        U: HttpResponseContent + Send + Sync + 'static,
+        F: FnOnce(T) -> Result<U, E>,
+    {
+        Ok(HttpResponseOk(f(self.0)?))
+    }
+}
+
 impl<T: HttpResponseContent + Send + Sync + 'static> HttpCodedResponse
     for HttpResponseOk<T>
 {
@@ -1362,6 +1433,35 @@ impl<
     pub fn headers_mut(&mut self) -> &mut HeaderMap {
         &mut self.other_headers
     }
+
+    /// Convert this response into one with a different body type parameter;
+    /// this may be useful when multiple, related endpoints return similar
+    /// response types that are convertible into a common type.
+    pub fn map<U, F>(self, f: F) -> HttpResponseHeaders<U, H>
+    where
+        U: HttpCodedResponse,
+        F: FnOnce(T) -> U,
+    {
+        HttpResponseHeaders {
+            body: f(self.body),
+            structured_headers: self.structured_headers,
+            other_headers: self.other_headers,
+        }
+    }
+
+    /// Similar to [`HttpResponseHeaders::map`] but with support for
+    /// fallibility.
+    pub fn try_map<U, E, F>(self, f: F) -> Result<HttpResponseHeaders<U, H>, E>
+    where
+        U: HttpCodedResponse,
+        F: FnOnce(T) -> Result<U, E>,
+    {
+        Ok(HttpResponseHeaders {
+            body: f(self.body)?,
+            structured_headers: self.structured_headers,
+            other_headers: self.other_headers,
+        })
+    }
 }
 impl<
         T: HttpCodedResponse,