diff --git a/src/Application.php b/src/Application.php
index 333c4fd..dcdabdb 100644
--- a/src/Application.php
+++ b/src/Application.php
@@ -96,10 +96,14 @@ public static function prettifyException(Throwable $e): Throwable
             $message = $body['message'] ?? 'Unknown Bref Cloud error';
             $statusCode = $e->getResponse()->getStatusCode();
 
-            $message = match ($statusCode) {
-                401 => 'Unauthenticated. Please log in with `bref login`.',
-                403 => 'Forbidden. You do not have the required permissions. Do you need to login to a different team?',
-                429 => 'Too many requests, try again in a minute.',
+            // Laravel's messages for a failed authorization, which say nothing about the cause
+            $isGenericForbidden = in_array($body['message'] ?? '', ['', 'This action is unauthorized.'], true);
+
+            $message = match (true) {
+                $statusCode === 401 => 'Unauthenticated. Please log in with `bref login`.',
+                // Other 403 responses explain their cause (e.g. Bref Cloud cannot access the AWS account)
+                $statusCode === 403 && $isGenericForbidden => 'Forbidden. You do not have the required permissions. Do you need to login to a different team?',
+                $statusCode === 429 => 'Too many requests, try again in a minute.',
                 default => $message,
             };
 
diff --git a/src/Commands/Connect.php b/src/Commands/Connect.php
index da9d344..3f2e5ff 100644
--- a/src/Commands/Connect.php
+++ b/src/Commands/Connect.php
@@ -3,6 +3,8 @@
 namespace Bref\Cli\Commands;
 
 use Aws\CloudFormation\CloudFormationClient;
+use Aws\Exception\AwsException;
+use Aws\Exception\CredentialsException;
 use Aws\Sts\StsClient;
 use Bref\Cli\BrefCloudClient;
 use Bref\Cli\Cli\IO;
@@ -24,7 +26,7 @@ protected function configure(): void
         $this
             ->setName('connect')
             ->setDescription('Connect an AWS account to Bref Cloud using the AWS credentials configured on your machine')
-            ->addOption('profile', null, InputOption::VALUE_REQUIRED, 'The AWS profile to use', 'default');
+            ->addOption('profile', null, InputOption::VALUE_REQUIRED, 'The AWS profile to use (defaults to the AWS_PROFILE environment variable, then to "default")');
     }
 
     protected function execute(InputInterface $input, OutputInterface $output): int
@@ -35,10 +37,14 @@ protected function execute(InputInterface $input, OutputInterface $output): int
             'Retrieving information...',
         ]);
 
-        /** @var string $awsProfile */
+        /** @var string|null $awsProfile */
         $awsProfile = $input->getOption('profile');
-
-        putenv('AWS_PROFILE=' . $awsProfile);
+        if ($awsProfile !== null) {
+            putenv('AWS_PROFILE=' . $awsProfile);
+        } else {
+            // Keep the profile selected with `export AWS_PROFILE=...`, like the AWS CLI
+            $awsProfile = getenv('AWS_PROFILE') ?: 'default';
+        }
 
         $accountId = $this->getCurrentAwsAccountId($awsProfile);
         // TODO verbose only
@@ -116,11 +122,15 @@ protected function execute(InputInterface $input, OutputInterface $output): int
             $stackParameters['RoleName'] = $details['role_name'];
         }
         $cloudFormation = new CloudFormation($cloudFormationClient);
-        $cloudFormation->deploy(
-            $details['stack_name'],
-            $details['template_url'],
-            $stackParameters,
-        );
+        try {
+            $cloudFormation->deploy(
+                $details['stack_name'],
+                $details['template_url'],
+                $stackParameters,
+            );
+        } catch (AwsException $e) {
+            throw self::explainDeployError($e, $details['stack_name'], $details['region']);
+        }
 
         if (!$isConnected && $accountName) {
             IO::spin('adding to Bref Cloud');
@@ -140,14 +150,49 @@ protected function execute(InputInterface $input, OutputInterface $output): int
         return 0;
     }
 
+    /**
+     * AWS accounts created with "Sign up for AWS (new)" (AWS projects) have AWS-managed service control
+     * policies: they deny CloudFormation outside of the project's region, and Bref Cloud could not
+     * access the account anyway. The raw AWS error does not say any of that.
+     */
+    public static function explainDeployError(AwsException $e, string $stackName, string $region): Exception
+    {
+        $awsMessage = $e->getAwsErrorMessage() ?: $e->getMessage();
+        if (! str_contains($awsMessage, 'explicit deny in a service control policy')) {
+            return $e;
+        }
+
+        return new Exception(
+            "AWS denied the deployment of the '$stackName' CloudFormation stack in $region: $awsMessage\n\n"
+            . 'If this AWS account was created with "Sign up for AWS (new)", it is an AWS project: AWS blocks Bref Cloud from connecting to AWS projects. '
+            . 'Create an AWS account with "Sign up for AWS (advanced)" instead: https://bref.sh/docs/setup#aws-projects',
+            previous: $e,
+        );
+    }
+
     private function getCurrentAwsAccountId(string $profile): string
     {
         $sts = new StsClient([
             'region' => 'us-east-1',
         ]);
 
-        return $sts->getCallerIdentity()->toArray()['Account'] ??
-            throw new RuntimeException('Could not determine the AWS account ID');
+        try {
+            $identity = $sts->getCallerIdentity()->toArray();
+        } catch (CredentialsException $e) {
+            // The AWS SDK tries each credential provider in turn and only reports the error of the last one
+            // (the EC2 instance metadata service), which hides the actual cause, e.g. an expired `aws login` session
+            if (str_contains($e->getMessage(), 'instance profile metadata service')) {
+                throw new Exception(
+                    "No valid AWS credentials found for the AWS profile '$profile'. "
+                    . "If you log in with `aws login`, run `aws login --profile $profile` again: its sessions expire after 12 hours. "
+                    . 'Use the `--profile` option to select another AWS profile.',
+                    previous: $e,
+                );
+            }
+            throw $e;
+        }
+
+        return $identity['Account'] ?? throw new RuntimeException('Could not determine the AWS account ID');
     }
 
     private function selectTeam(BrefCloudClient $brefCloud): int
diff --git a/tests/ApplicationTest.php b/tests/ApplicationTest.php
new file mode 100644
index 0000000..4888aa3
--- /dev/null
+++ b/tests/ApplicationTest.php
@@ -0,0 +1,46 @@
+<?php declare(strict_types=1);
+
+namespace Bref\Cli\Test;
+
+use Bref\Cli\Application;
+use PHPUnit\Framework\TestCase;
+use Symfony\Component\HttpClient\Exception\ClientException;
+use Symfony\Component\HttpClient\MockHttpClient;
+use Symfony\Component\HttpClient\Response\MockResponse;
+
+class ApplicationTest extends TestCase
+{
+    public function test_a_forbidden_error_shows_the_message_of_the_api(): void
+    {
+        $e = Application::prettifyException($this->apiError(403, [
+            'message' => 'Bref Cloud is not authorized to access the AWS account "production": it could not assume the role arn:aws:iam::123456789012:role/BrefCloudAccess.',
+        ]));
+
+        $this->assertSame(
+            'Bref Cloud API error: [403] Bref Cloud is not authorized to access the AWS account "production": it could not assume the role arn:aws:iam::123456789012:role/BrefCloudAccess.',
+            $e->getMessage(),
+        );
+    }
+
+    public function test_a_failed_authorization_suggests_logging_in_to_another_team(): void
+    {
+        $expected = 'Bref Cloud API error: [403] Forbidden. You do not have the required permissions. Do you need to login to a different team?';
+
+        $this->assertSame($expected, Application::prettifyException($this->apiError(403, ['message' => 'This action is unauthorized.']))->getMessage());
+        $this->assertSame($expected, Application::prettifyException($this->apiError(403, ['message' => '']))->getMessage());
+        $this->assertSame($expected, Application::prettifyException($this->apiError(403, []))->getMessage());
+    }
+
+    /**
+     * @param array<string, mixed> $body
+     */
+    private function apiError(int $statusCode, array $body): ClientException
+    {
+        $client = new MockHttpClient(new MockResponse(json_encode($body, JSON_THROW_ON_ERROR), [
+            'http_code' => $statusCode,
+            'response_headers' => ['content-type' => 'application/json'],
+        ]));
+
+        return new ClientException($client->request('POST', 'https://bref.cloud/api/v1/deployments'));
+    }
+}
diff --git a/tests/Commands/ConnectTest.php b/tests/Commands/ConnectTest.php
new file mode 100644
index 0000000..87f6b4a
--- /dev/null
+++ b/tests/Commands/ConnectTest.php
@@ -0,0 +1,38 @@
+<?php declare(strict_types=1);
+
+namespace Bref\Cli\Test\Commands;
+
+use Aws\Command;
+use Aws\Exception\AwsException;
+use Bref\Cli\Commands\Connect;
+use PHPUnit\Framework\TestCase;
+
+class ConnectTest extends TestCase
+{
+    public function test_a_denial_by_a_service_control_policy_explains_aws_projects(): void
+    {
+        $awsError = $this->awsError('User: arn:aws:sts::123456789012:assumed-role/AccountFullAccessRole/abc is not authorized to perform: cloudformation:DescribeStacks on resource: arn:aws:cloudformation:us-east-1:123456789012:stack/bref-cloud-connect/* with an explicit deny in a service control policy: arn:aws:organizations::111111111111:policy/o-abc/service_control_policy/p-abc');
+
+        $e = Connect::explainDeployError($awsError, 'bref-cloud-connect', 'us-east-1');
+
+        $this->assertStringStartsWith("AWS denied the deployment of the 'bref-cloud-connect' CloudFormation stack in us-east-1: User: arn:aws:sts::123456789012:assumed-role/AccountFullAccessRole/abc is not authorized", $e->getMessage());
+        $this->assertStringContainsString('"Sign up for AWS (new)", it is an AWS project', $e->getMessage());
+        $this->assertStringContainsString('https://bref.sh/docs/setup#aws-projects', $e->getMessage());
+        $this->assertSame($awsError, $e->getPrevious());
+    }
+
+    public function test_other_aws_errors_are_left_unchanged(): void
+    {
+        $awsError = $this->awsError('Stack with id bref-cloud-connect does not exist');
+
+        $this->assertSame($awsError, Connect::explainDeployError($awsError, 'bref-cloud-connect', 'us-east-1'));
+    }
+
+    private function awsError(string $awsMessage): AwsException
+    {
+        return new AwsException('Error executing "DescribeStacks"; AWS HTTP error: ' . $awsMessage, new Command('DescribeStacks'), [
+            'code' => 'AccessDenied',
+            'message' => $awsMessage,
+        ]);
+    }
+}