diff --git a/sqlx-core/Cargo.toml b/sqlx-core/Cargo.toml
index f4db49fa7a..bb58e5674f 100644
--- a/sqlx-core/Cargo.toml
+++ b/sqlx-core/Cargo.toml
@@ -34,14 +34,15 @@ decimal = [ "rust_decimal", "num-bigint" ]
 json = [ "serde", "serde_json" ]
 
 # runtimes
-runtime-actix-native-tls = [ "sqlx-rt/runtime-actix-native-tls", "_rt-actix" ]
-runtime-async-std-native-tls = [ "sqlx-rt/runtime-async-std-native-tls", "_rt-async-std" ]
-runtime-tokio-native-tls = [ "sqlx-rt/runtime-tokio-native-tls", "_rt-tokio" ]
+runtime-actix-native-tls = [ "sqlx-rt/runtime-actix-native-tls", "_tls-native-tls", "_rt-actix" ]
+runtime-async-std-native-tls = [ "sqlx-rt/runtime-async-std-native-tls", "_tls-native-tls", "_rt-async-std" ]
+runtime-tokio-native-tls = [ "sqlx-rt/runtime-tokio-native-tls", "_tls-native-tls", "_rt-tokio" ]
 
 # for conditional compilation
 _rt-actix = []
 _rt-async-std = []
 _rt-tokio = []
+_tls-native-tls = []
 
 # support offline/decoupled building (enables serialization of `Describe`)
 offline = [ "serde", "either/serde" ]
diff --git a/sqlx-core/src/error.rs b/sqlx-core/src/error.rs
index ff9b05edd2..0cab5a2f85 100644
--- a/sqlx-core/src/error.rs
+++ b/sqlx-core/src/error.rs
@@ -129,12 +129,6 @@ impl Error {
     pub(crate) fn config(err: impl StdError + Send + Sync + 'static) -> Self {
         Error::Configuration(err.into())
     }
-
-    #[allow(dead_code)]
-    #[inline]
-    pub(crate) fn tls(err: impl StdError + Send + Sync + 'static) -> Self {
-        Error::Tls(err.into())
-    }
 }
 
 pub(crate) fn mismatched_types<DB: Database, T: Type<DB>>(ty: &DB::TypeInfo) -> BoxDynError {
@@ -240,6 +234,14 @@ impl From<crate::migrate::MigrateError> for Error {
     }
 }
 
+#[cfg(feature = "_tls-native-tls")]
+impl From<sqlx_rt::native_tls::Error> for Error {
+    #[inline]
+    fn from(error: sqlx_rt::native_tls::Error) -> Self {
+        Error::Tls(Box::new(error))
+    }
+}
+
 // Format an error message as a `Protocol` error
 macro_rules! err_protocol {
     ($expr:expr) => {
diff --git a/sqlx-core/src/net/tls.rs b/sqlx-core/src/net/tls.rs
index 674babfa49..69041b4699 100644
--- a/sqlx-core/src/net/tls.rs
+++ b/sqlx-core/src/net/tls.rs
@@ -48,17 +48,17 @@ where
         if !accept_invalid_certs {
             if let Some(ca) = root_cert_path {
                 let data = fs::read(ca).await?;
-                let cert = Certificate::from_pem(&data).map_err(Error::tls)?;
+                let cert = Certificate::from_pem(&data)?;
 
                 builder.add_root_certificate(cert);
             }
         }
 
         #[cfg(not(feature = "_rt-async-std"))]
-        let connector = builder.build().map_err(Error::tls)?;
+        let connector = sqlx_rt::TlsConnector::from(builder.build()?);
 
         #[cfg(feature = "_rt-async-std")]
-        let connector = builder;
+        let connector = sqlx_rt::TlsConnector::from(builder);
 
         let stream = match replace(self, MaybeTlsStream::Upgrading) {
             MaybeTlsStream::Raw(stream) => stream,
@@ -75,12 +75,7 @@ where
             }
         };
 
-        *self = MaybeTlsStream::Tls(
-            sqlx_rt::TlsConnector::from(connector)
-                .connect(host, stream)
-                .await
-                .map_err(|err| Error::Tls(err.into()))?,
-        );
+        *self = MaybeTlsStream::Tls(connector.connect(host, stream).await?);
 
         Ok(())
     }