diff --git a/moto/organizations/exceptions.py b/moto/organizations/exceptions.py
index 10fb8ecbedb3..4ca0fcf64931 100644
--- a/moto/organizations/exceptions.py
+++ b/moto/organizations/exceptions.py
@@ -40,6 +40,14 @@ def __init__(self) -> None:
         )
 
 
+class AlreadyInOrganizationException(JsonRESTError):
+    code = 400
+
+    def __init__(self) -> None:
+        super().__init__(
+            "AlreadyInOrganizationException", "The provided account is already a member of an organization."
+        )
+
 class AWSOrganizationsNotInUseException(JsonRESTError):
     code = 400
 
@@ -83,6 +91,15 @@ def __init__(self) -> None:
         )
 
 
+class OrganizationNotEmptyException(JsonRESTError):
+    code = 400
+
+    def __init__(self) -> None:
+        super().__init__(
+            "OrganizationNotEmptyException", "To delete an organization you must first remove all member accounts (except the master).",
+        )
+
+
 class PolicyTypeAlreadyEnabledException(JsonRESTError):
     code = 400
 
diff --git a/moto/organizations/models.py b/moto/organizations/models.py
index d84f0ca2e1e9..29bbb5e98683 100644
--- a/moto/organizations/models.py
+++ b/moto/organizations/models.py
@@ -21,7 +21,7 @@
     PolicyTypeAlreadyEnabledException,
     PolicyTypeNotEnabledException,
     RootNotFoundException,
-    TargetNotFoundException,
+    TargetNotFoundException, AlreadyInOrganizationException, OrganizationNotEmptyException,
 )
 from moto.utilities.paginator import paginate
 from moto.utilities.utils import PARTITION_NAMES, get_partition
@@ -422,6 +422,9 @@ def _get_root_by_id(self, root_id: str) -> FakeRoot:
         return root  # type: ignore[return-value]
 
     def create_organization(self, region: str, **kwargs: Any) -> Dict[str, Any]:
+        if self.org or self.account_id in organizations_backends.master_accounts:
+            raise AlreadyInOrganizationException
+
         self.org = FakeOrganization(
             self.account_id,
             region_name=region,
@@ -468,11 +471,12 @@ def describe_organization(self) -> Dict[str, Any]:
         raise AWSOrganizationsNotInUseException
 
     def delete_organization(self) -> None:
+        if self.org is None:
+            raise AWSOrganizationsNotInUseException
+
         if [account for account in self.accounts if account.name != "master"]:
-            raise RESTError(
-                "OrganizationNotEmptyException",
-                "To delete an organization you must first remove all member accounts (except the master).",
-            )
+            raise OrganizationNotEmptyException
+
         self._reset()
 
     def list_roots(self) -> Dict[str, Any]:
@@ -532,6 +536,9 @@ def list_organizational_units_for_parent(
         ]
 
     def create_account(self, **kwargs: Any) -> Dict[str, Any]:
+        if self.org is None or self.account_id not in organizations_backends.master_accounts:
+            raise AWSOrganizationsNotInUseException
+
         new_account = FakeAccount(self.org, **kwargs)  # type: ignore
         self.accounts.append(new_account)
         self.attach_policy(PolicyId=utils.DEFAULT_POLICY_ID, TargetId=new_account.id)
@@ -542,6 +549,9 @@ def create_account(self, **kwargs: Any) -> Dict[str, Any]:
         return new_account.create_account_status
 
     def close_account(self, **kwargs: Any) -> None:
+        if self.org is None or self.account_id not in organizations_backends.master_accounts:
+            raise AWSOrganizationsNotInUseException
+
         for account in self.accounts:
             if account.id == kwargs["AccountId"]:
                 account.close()