diff --git a/openssl/src/crypto/pkey.rs b/openssl/src/crypto/pkey.rs
index bbb8427d..15744047 100644
--- a/openssl/src/crypto/pkey.rs
+++ b/openssl/src/crypto/pkey.rs
@@ -103,9 +103,11 @@ impl PKey {
     ///
     /// The callback will be passed the password buffer and should return the number of characters
     /// placed into the buffer.
+    ///
+    /// Requires the `catch_unwind` feature.
     #[cfg(feature = "catch_unwind")]
     pub fn private_key_from_pem_cb<R, F>(reader: &mut R, pass_cb: F) -> Result<PKey, SslError>
-        where R: Read, F: FnMut(&mut [c_char]) -> usize
+        where R: Read, F: FnOnce(&mut [c_char]) -> usize
     {
         let mut cb = CallbackState::new(pass_cb);
 
diff --git a/openssl/src/crypto/rsa.rs b/openssl/src/crypto/rsa.rs
index 9a04bf7f..3b420fbc 100644
--- a/openssl/src/crypto/rsa.rs
+++ b/openssl/src/crypto/rsa.rs
@@ -82,9 +82,11 @@ impl RSA {
     }
 
     /// Reads an RSA private key from PEM formatted data and supplies a password callback.
+    ///
+    /// Requires the `catch_unwind` feature.
     #[cfg(feature = "catch_unwind")]
     pub fn private_key_from_pem_cb<R, F>(reader: &mut R, pass_cb: F) -> Result<RSA, SslError>
-        where R: Read, F: FnMut(&mut [c_char]) -> usize
+        where R: Read, F: FnOnce(&mut [c_char]) -> usize
     {
         let mut cb = CallbackState::new(pass_cb);
 
diff --git a/openssl/src/crypto/util.rs b/openssl/src/crypto/util.rs
index 85df86b7..be72aa59 100644
--- a/openssl/src/crypto/util.rs
+++ b/openssl/src/crypto/util.rs
@@ -41,7 +41,7 @@ pub extern "C" fn invoke_passwd_cb<F>(buf: *mut c_char,
                                       _rwflag: c_int,
                                       cb_state: *mut c_void)
                                       -> c_int
-                                      where F: FnMut(&mut [i8]) -> usize {
+                                      where F: FnOnce(&mut [i8]) -> usize {
     let result = panic::catch_unwind(|| {
         // build a `i8` slice to pass to the user callback
         let pass_slice = unsafe { slice::from_raw_parts_mut(buf, size as usize) };