diff --git a/exporters/ostream/src/log_exporter.cc b/exporters/ostream/src/log_exporter.cc
index c11ec13786..59cbe7cda4 100644
--- a/exporters/ostream/src/log_exporter.cc
+++ b/exporters/ostream/src/log_exporter.cc
@@ -149,7 +149,7 @@ sdk::common::ExportResult OStreamLogExporter::Export(
           << "  severity_num  : " << static_cast<int>(log_record->GetSeverity()) << "\n"
           << "  severity_text : ";
 
-    int severity_index = static_cast<int>(log_record->GetSeverity());
+    std::size_t severity_index = static_cast<std::size_t>(log_record->GetSeverity());
     if (severity_index < 0 ||
         severity_index >= std::extent<decltype(opentelemetry::logs::SeverityNumToText)>::value)
     {
@@ -181,7 +181,7 @@ sdk::common::ExportResult OStreamLogExporter::Export(
   return sdk::common::ExportResult::kSuccess;
 }
 
-bool OStreamLogExporter::Shutdown(std::chrono::microseconds timeout) noexcept
+bool OStreamLogExporter::Shutdown(std::chrono::microseconds) noexcept
 {
   const std::lock_guard<opentelemetry::common::SpinLockMutex> locked(lock_);
   is_shutdown_ = true;
diff --git a/exporters/otlp/src/otlp_http_client.cc b/exporters/otlp/src/otlp_http_client.cc
index 2e66c8373c..5fa2c7cf8b 100644
--- a/exporters/otlp/src/otlp_http_client.cc
+++ b/exporters/otlp/src/otlp_http_client.cc
@@ -595,8 +595,7 @@ OtlpHttpClient::~OtlpHttpClient()
 {
   if (!isShutdown())
   {
-    Shutdown(std::chrono::duration_cast<std::chrono::microseconds>(
-        std::chrono::steady_clock::time_point::max() - std::chrono::steady_clock::now()));
+    Shutdown();
   }
 
   // Wait for all the sessions to finish
@@ -756,10 +755,20 @@ bool OtlpHttpClient::Shutdown(std::chrono::microseconds timeout) noexcept
 
   // Wait for all the sessions to finish
   std::unique_lock<std::mutex> lock(session_waker_lock_);
-  session_waker_.wait_for(lock, timeout, [this] {
-    std::lock_guard<std::recursive_mutex> guard{session_manager_lock_};
-    return running_sessions_.empty();
-  });
+  if (timeout == std::chrono::microseconds::zero())
+  {
+    session_waker_.wait(lock, [this] {
+      std::lock_guard<std::recursive_mutex> guard{session_manager_lock_};
+      return running_sessions_.empty();
+    });
+  }
+  else
+  {
+    session_waker_.wait_for(lock, timeout, [this] {
+      std::lock_guard<std::recursive_mutex> guard{session_manager_lock_};
+      return running_sessions_.empty();
+    });
+  }
 
   while (cleanupGCSessions())
     ;