diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index f55543a7..0149e8ab 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -14,17 +14,17 @@ jobs:
       fail-fast: false
       matrix:
         include:
-          - erlang: "28.1"
-            elixir: "1.19"
+          - erlang: "29.0"
+            elixir: "1.20"
             lint: true
             coverage: true
             dialyzer: true
           # One version down.
-          - erlang: "27.2"
-            elixir: "1.18"
+          - erlang: "28.1"
+            elixir: "1.19"
           # Oldest version.
           - erlang: "24.3"
-            elixir: "1.12.3"
+            elixir: "1.15.8"
 
     env:
       GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
diff --git a/mix.exs b/mix.exs
index aabe70ba..f0ddd8d4 100644
--- a/mix.exs
+++ b/mix.exs
@@ -8,7 +8,7 @@ defmodule Mint.MixProject do
     [
       app: :mint,
       version: @version,
-      elixir: "~> 1.12",
+      elixir: "~> 1.15",
       start_permanent: Mix.env() == :prod,
       elixirc_paths: elixirc_paths(Mix.env()),
       deps: deps(),
diff --git a/test/mint/http1/integration_test.exs b/test/mint/http1/integration_test.exs
index 6c740711..d78bfb77 100644
--- a/test/mint/http1/integration_test.exs
+++ b/test/mint/http1/integration_test.exs
@@ -224,9 +224,12 @@ defmodule Mint.HTTP1.IntegrationTest do
                  transport_opts: [log_alert: false, reuse_sessions: false]
                )
 
-      # OTP 21.3 changes the format of SSL errors. Let's support both ways for now.
+      # OTP 21.3 changes the format of SSL errors. OTP 29 reports a hostname
+      # mismatch as a "bad certificate" alert instead of "handshake failure".
+      # Support all the variants.
       assert reason == {:tls_alert, ~c"handshake failure"} or
-               match?({:tls_alert, {:handshake_failure, _}}, reason)
+               match?({:tls_alert, {:handshake_failure, _}}, reason) or
+               match?({:tls_alert, {:bad_certificate, _}}, reason)
 
       assert {:ok, _conn} =
                HTTP1.connect(:https, "wrong.host.badssl.com", 443,
diff --git a/test/mint/integration_test.exs b/test/mint/integration_test.exs
index 619dfecf..af7b44db 100644
--- a/test/mint/integration_test.exs
+++ b/test/mint/integration_test.exs
@@ -80,9 +80,12 @@ defmodule Mint.IntegrationTest do
                  transport_opts: [log_alert: false, reuse_sessions: false]
                )
 
-      # OTP 21.3 changes the format of SSL errors. Let's support both ways for now.
+      # OTP 21.3 changes the format of SSL errors. OTP 29 reports a hostname
+      # mismatch as a "bad certificate" alert instead of "handshake failure".
+      # Support all the variants.
       assert reason == {:tls_alert, ~c"handshake failure"} or
-               match?({:tls_alert, {:handshake_failure, _}}, reason)
+               match?({:tls_alert, {:handshake_failure, _}}, reason) or
+               match?({:tls_alert, {:bad_certificate, _}}, reason)
 
       assert {:ok, _conn} =
                HTTP.connect(