diff --git a/lib/docker/container.rb b/lib/docker/container.rb
index 3c0cc044..10ea8d98 100644
--- a/lib/docker/container.rb
+++ b/lib/docker/container.rb
@@ -60,8 +60,11 @@ def exec(command, options = {}, &block)
     detach = options.delete(:detach) || false
     user = options.delete(:user)
     stdin = options.delete(:stdin)
-    stdout = options.delete(:stdout) || !detach
-    stderr = options.delete(:stderr) || !detach
+    # `options.delete(:stdout) || !detach` turns an explicit false back into
+    # true, so these have to be tested for presence rather than truthiness.
+    # They default to the inverse of :detach when the caller says nothing.
+    stdout = options.key?(:stdout) ? options.delete(:stdout) : !detach
+    stderr = options.key?(:stderr) ? options.delete(:stderr) : !detach
     wait = options.delete(:wait)
 
     opts = {
diff --git a/spec/docker/container_spec.rb b/spec/docker/container_spec.rb
index d5c8a34f..f27b1c05 100644
--- a/spec/docker/container_spec.rb
+++ b/spec/docker/container_spec.rb
@@ -578,6 +578,30 @@
       end
     end
 
+    # `stderr = options.delete(:stderr) || !detach` turns an explicit false back
+    # into true, so both stream options were impossible to switch off.
+    context 'when stderr is false' do
+      let(:output) {
+        subject.exec(['bash', '-c', 'echo out; echo err 1>&2'], stderr: false)
+      }
+
+      it 'captures stdout but not stderr' do
+        expect(output[0]).to eq(["out\n"])
+        expect(output[1]).to be_empty
+      end
+    end
+
+    context 'when stdout is false' do
+      let(:output) {
+        subject.exec(['bash', '-c', 'echo out; echo err 1>&2'], stdout: false)
+      }
+
+      it 'captures stderr but not stdout' do
+        expect(output[0]).to be_empty
+        expect(output[1]).to eq(["err\n"])
+      end
+    end
+
     context 'when passed a block' do
       it 'streams the stdout/stderr messages' do
         chunk = nil