diff --git a/doc/requirements-and-limitations.md b/doc/requirements-and-limitations.md
index 81e7226..7d246a8 100644
--- a/doc/requirements-and-limitations.md
+++ b/doc/requirements-and-limitations.md
@@ -30,11 +30,12 @@ The `SUPER` privilege is required for `STOP SLAVE`, `START SLAVE` operations. Th
 
 - MySQL 5.7 `JSON` columns are not supported. They are likely to be supported shortly.
 
-- The two _before_ & _after_ tables must share some `UNIQUE KEY`. Such key would be used by `gh-ost` to iterate the table.
-  - As an example, if your table has a single `UNIQUE KEY` and no `PRIMARY KEY`, and you wish to replace it with a `PRIMARY KEY`, you will need two migrations: one to add the `PRIMARY KEY` (this migration will use the existing `UNIQUE KEY`), another to drop the now redundant `UNIQUE KEY` (this migration will use the `PRIMARY KEY`).
-
-- The chosen migration key must not include columns with `NULL` values.
-  - `gh-ost` will do its best to pick a migration key with non-nullable columns. It will by default refuse a migration where the only possible `UNIQUE KEY` includes nullable-columns. You may override this refusal via `--allow-nullable-unique-key` but **you must** be sure there are no actual `NULL` values in those columns. Such `NULL` values would cause a data integrity problem and potentially a corrupted migration.
+- The two _before_ & _after_ tables must share a `PRIMARY KEY` or other `UNIQUE KEY`. This key will be used by `gh-ost` to iterate through the table rows when copying. [Read more](shared-key.md)
+  - The migration key must not include columns with NULL values. This means either:
+    1. The columns are `NOT NULL`, or
+    2. The columns are nullable but don't contain any NULL values.
+  - by default, `gh-ost` will not run if the only `UNIQUE KEY` includes nullable columns.
+    - You may override this via `--allow-nullable-unique-key` but make sure there are no actual `NULL` values in those columns. Existing NULL values can't guarantee data integrity on the migrated table.
 
 - It is not allowed to migrate a table where another table exists with same name and different upper/lower case.
   - For example, you may not migrate `MyTable` if another table called `MYtable` exists in the same schema.
@@ -48,4 +49,4 @@ The `SUPER` privilege is required for `STOP SLAVE`, `START SLAVE` operations. Th
 
 - If you have en `enum` field as part of your migration key (typically the `PRIMARY KEY`), migration performance will be degraded and potentially bad. [Read more](https://github.com/github/gh-ost/pull/277#issuecomment-254811520)
 
-- Migrating a `FEDERATED` table is unsupported and is irrelevant to the problem `gh-ost` tackles. 
+- Migrating a `FEDERATED` table is unsupported and is irrelevant to the problem `gh-ost` tackles.
diff --git a/doc/shared-key.md b/doc/shared-key.md
new file mode 100644
index 0000000..480ad97
--- /dev/null
+++ b/doc/shared-key.md
@@ -0,0 +1,68 @@
+# Shared key
+
+A requirement for a migration to run is that the two _before_ and _after_ tables have a shared unique key. This is to elaborate and illustrate on the matter.
+
+### Introduction
+
+Consider a classic, simple migration. The table is any normal:
+
+```
+CREATE TABLE tbl (
+  id bigint unsigned not null auto_increment,
+  data varchar(255),
+  more_data int,
+  PRIMARY KEY(id)
+)
+```
+
+And the migration is a simple `add column ts timestamp`.
+
+In such migration there is no change in indexes, and in particular no change to any unique key, and specifically no change to the `PRIMARY KEY`. To run this migration, `gh-ost` would iterate the `tbl` table using the primary key, copy rows from `tbl` to the _ghost_ table `_tbl_gho` by order of `id`, and then apply binlog events onto `_tbl_gho`.
+
+Applying the binlog events assumes the existence of a shared unique key. For example, an `UPDATE` statement in the binary log translate to a `REPLACE` statement which `gh-ost` applies to the _ghost_ table. Such statement expects to add or replace an existing row based on given row data. In particular, it would _replace_ an existing row if a unique key violation is met.
+
+So `gh-ost` correlates `tbl` and `_tbl_gho` rows using a unique key. In the above example that would be the `PRIMARY KEY`.
+
+### Rules
+
+There must be a shared set of not-null columns for which there is a unique constraint in both the original table and the migration (_ghost_) table.
+
+### Interpreting the rules
+
+The same columns must be covered by a unique key in both tables. This doesn't have to be the `PRIMARY KEY`. This doesn't have to be a key of the same name.
+
+Upon migration, `gh-ost` inspects both the original and _ghost_ table and attempts to find at least one such unique key (or rather, a set of columns) that is shared between the two. Typically this would just be the `PRIMARY KEY`, but sometimes you may change the `PRIMARY KEY` itself, in which case `gh-ost` will look for other options.
+
+`gh-ost` expects unique keys where no `NULL` values are found, i.e. all columns covered by the unique key are defined as `NOT NULL`. This is implicitly true for `PRIMARY KEY`s. If no such key can be found, `gh-ost` bails out. In the event there is no such key, but you happen to _know_ your columns have no `NULL` values even though they're `NULL`-able, you may take responsibility and pass the `--allow-nullable-unique-key`. The migration will run well as long as no `NULL` values are found in the unique key's columns. Any actual `NULL`s may corrupt the migration.
+
+### Examples: allowed and not allowed
+
+```
+create table some_table (
+  id int auto_increment,
+  ts timestamp,
+  name varchar(128) not null,
+  owner_id int not null,
+  loc_id int,
+  primary key(id),
+  unique key name_uidx(name)
+)
+```
+
+Following are examples of migrations that are _good to run_:
+
+- `add column i int`
+- `add key owner_idx(owner_id)`
+- `add unique key owner_name_idx(owner_id, name)` - though you need to make sure to not write conflicting rows while this migration runs
+- `drop key name_uidx` - `primary key` is shared between the tables
+- `drop primary key, add primary key(owner_id, loc_id)` - `name_uidx` is shared between the tables and is used for migration
+- `change id bigint unsigned` - the `'primary key` is used. The change of type still makes the `primary key` workable.
+- `drop primary key, drop key name_uidx, create primary key(name), create unique key id_uidx(id)` - swapping the two keys. `gh-ost` is still happy because `id` is still unique in both tables. So is `name`.
+
+
+Following are examples of migrations that _cannot run_:
+
+- `drop primary key, drop key name_uidx` - no unique key to _ghost_ table, so clearly cannot run
+- `drop primary key, drop key name_uidx, create primary key(name, owner_id)` - no shared columns to both tables. Even though `name` exists in the _ghost_ table's `primary key`, it is only part of the key and in itself does not guarantee uniqueness in the _ghost_ table.
+
+Also, you cannot run a migration on a table that doesn't have some form of `unique key` in the first place, such as `some_table (id int, ts timestamp)`
diff --git a/localtests/fail-drop-pk/create.sql b/localtests/fail-drop-pk/create.sql
new file mode 100644
index 0000000..5bb45f2
--- /dev/null
+++ b/localtests/fail-drop-pk/create.sql
@@ -0,0 +1,22 @@
+drop table if exists gh_ost_test;
+create table gh_ost_test (
+  id int auto_increment,
+  i int not null,
+  ts timestamp,
+  primary key(id)
+) auto_increment=1;
+
+drop event if exists gh_ost_test;
+delimiter ;;
+create event gh_ost_test
+  on schedule every 1 second
+  starts current_timestamp
+  ends current_timestamp + interval 60 second
+  on completion not preserve
+  enable
+  do
+begin
+  insert into gh_ost_test values (null, 11, now());
+  insert into gh_ost_test values (null, 13, now());
+  insert into gh_ost_test values (null, 17, now());
+end ;;
diff --git a/localtests/fail-drop-pk/expect_failure b/localtests/fail-drop-pk/expect_failure
new file mode 100644
index 0000000..021ae87
--- /dev/null
+++ b/localtests/fail-drop-pk/expect_failure
@@ -0,0 +1 @@
+No PRIMARY nor UNIQUE key found in table
diff --git a/localtests/fail-drop-pk/extra_args b/localtests/fail-drop-pk/extra_args
new file mode 100644
index 0000000..2017cbc
--- /dev/null
+++ b/localtests/fail-drop-pk/extra_args
@@ -0,0 +1 @@
+--alter="change id id int, drop primary key" 
diff --git a/localtests/fail-no-shared-uk/create.sql b/localtests/fail-no-shared-uk/create.sql
new file mode 100644
index 0000000..5bb45f2
--- /dev/null
+++ b/localtests/fail-no-shared-uk/create.sql
@@ -0,0 +1,22 @@
+drop table if exists gh_ost_test;
+create table gh_ost_test (
+  id int auto_increment,
+  i int not null,
+  ts timestamp,
+  primary key(id)
+) auto_increment=1;
+
+drop event if exists gh_ost_test;
+delimiter ;;
+create event gh_ost_test
+  on schedule every 1 second
+  starts current_timestamp
+  ends current_timestamp + interval 60 second
+  on completion not preserve
+  enable
+  do
+begin
+  insert into gh_ost_test values (null, 11, now());
+  insert into gh_ost_test values (null, 13, now());
+  insert into gh_ost_test values (null, 17, now());
+end ;;
diff --git a/localtests/fail-no-shared-uk/expect_failure b/localtests/fail-no-shared-uk/expect_failure
new file mode 100644
index 0000000..d3ef0f1
--- /dev/null
+++ b/localtests/fail-no-shared-uk/expect_failure
@@ -0,0 +1 @@
+No shared unique key can be found after ALTER
diff --git a/localtests/fail-no-shared-uk/extra_args b/localtests/fail-no-shared-uk/extra_args
new file mode 100644
index 0000000..379a77d
--- /dev/null
+++ b/localtests/fail-no-shared-uk/extra_args
@@ -0,0 +1 @@
+--alter="drop primary key, add primary key (id, i)" 
diff --git a/localtests/swap-pk-uk/create.sql b/localtests/swap-pk-uk/create.sql
new file mode 100644
index 0000000..aa712b8
--- /dev/null
+++ b/localtests/swap-pk-uk/create.sql
@@ -0,0 +1,24 @@
+drop table if exists gh_ost_test;
+create table gh_ost_test (
+  id bigint,
+  i int not null,
+  ts timestamp(6),
+  primary key(id),
+  unique key its_uidx(i, ts)
+) ;
+
+drop event if exists gh_ost_test;
+delimiter ;;
+create event gh_ost_test
+  on schedule every 1 second
+  starts current_timestamp
+  ends current_timestamp + interval 60 second
+  on completion not preserve
+  enable
+  do
+begin
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 0, 11, now(6));
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 1, 13, now(6));
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 2, 17, now(6));
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 3, 19, now(6));
+end ;;
diff --git a/localtests/swap-pk-uk/extra_args b/localtests/swap-pk-uk/extra_args
new file mode 100644
index 0000000..f4de64a
--- /dev/null
+++ b/localtests/swap-pk-uk/extra_args
@@ -0,0 +1 @@
+--alter="drop primary key, drop key its_uidx, add primary key (i, ts), add unique key id_uidx(id)" 
diff --git a/localtests/swap-pk-uk/order_by b/localtests/swap-pk-uk/order_by
new file mode 100644
index 0000000..074d1ee
--- /dev/null
+++ b/localtests/swap-pk-uk/order_by
@@ -0,0 +1 @@
+id
diff --git a/localtests/swap-uk-uk/create.sql b/localtests/swap-uk-uk/create.sql
new file mode 100644
index 0000000..5fcbf32
--- /dev/null
+++ b/localtests/swap-uk-uk/create.sql
@@ -0,0 +1,24 @@
+drop table if exists gh_ost_test;
+create table gh_ost_test (
+  id bigint,
+  i int not null,
+  ts timestamp(6),
+  unique key id_uidx(id),
+  unique key its_uidx(i, ts)
+) ;
+
+drop event if exists gh_ost_test;
+delimiter ;;
+create event gh_ost_test
+  on schedule every 1 second
+  starts current_timestamp
+  ends current_timestamp + interval 60 second
+  on completion not preserve
+  enable
+  do
+begin
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 0, 11, now(6));
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 1, 13, now(6));
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 2, 17, now(6));
+  insert into gh_ost_test values ((unix_timestamp() << 2) + 3, 19, now(6));
+end ;;
diff --git a/localtests/swap-uk-uk/extra_args b/localtests/swap-uk-uk/extra_args
new file mode 100644
index 0000000..84161a5
--- /dev/null
+++ b/localtests/swap-uk-uk/extra_args
@@ -0,0 +1 @@
+--alter="drop key id_uidx, drop key its_uidx, add unique key its2_uidx(i, ts), add unique key id2_uidx(id)" 
diff --git a/localtests/swap-uk-uk/order_by b/localtests/swap-uk-uk/order_by
new file mode 100644
index 0000000..074d1ee
--- /dev/null
+++ b/localtests/swap-uk-uk/order_by
@@ -0,0 +1 @@
+id
diff --git a/localtests/swap-uk/create.sql b/localtests/swap-uk/create.sql
new file mode 100644
index 0000000..5bb45f2
--- /dev/null
+++ b/localtests/swap-uk/create.sql
@@ -0,0 +1,22 @@
+drop table if exists gh_ost_test;
+create table gh_ost_test (
+  id int auto_increment,
+  i int not null,
+  ts timestamp,
+  primary key(id)
+) auto_increment=1;
+
+drop event if exists gh_ost_test;
+delimiter ;;
+create event gh_ost_test
+  on schedule every 1 second
+  starts current_timestamp
+  ends current_timestamp + interval 60 second
+  on completion not preserve
+  enable
+  do
+begin
+  insert into gh_ost_test values (null, 11, now());
+  insert into gh_ost_test values (null, 13, now());
+  insert into gh_ost_test values (null, 17, now());
+end ;;
diff --git a/localtests/swap-uk/extra_args b/localtests/swap-uk/extra_args
new file mode 100644
index 0000000..ad80561
--- /dev/null
+++ b/localtests/swap-uk/extra_args
@@ -0,0 +1 @@
+--alter="drop primary key, add unique key(id)" 
diff --git a/localtests/test.sh b/localtests/test.sh
index eb0274a..c0b97a5 100755
--- a/localtests/test.sh
+++ b/localtests/test.sh
@@ -59,12 +59,16 @@ test_single() {
   fi
   orig_columns="*"
   ghost_columns="*"
+  order_by=""
   if [ -f $tests_path/$test_name/orig_columns ] ; then
     orig_columns=$(cat $tests_path/$test_name/orig_columns)
   fi
   if [ -f $tests_path/$test_name/ghost_columns ] ; then
     ghost_columns=$(cat $tests_path/$test_name/ghost_columns)
   fi
+  if [ -f $tests_path/$test_name/order_by ] ; then
+    order_by="order by $(cat $tests_path/$test_name/order_by)"
+  fi
   # graceful sleep for replica to catch up
   echo_dot
   sleep 1
@@ -129,8 +133,8 @@ test_single() {
   fi
 
   echo_dot
-  orig_checksum=$(gh-ost-test-mysql-replica --default-character-set=utf8mb4 test -e "select ${orig_columns} from gh_ost_test" -ss | md5sum)
-  ghost_checksum=$(gh-ost-test-mysql-replica --default-character-set=utf8mb4 test -e "select ${ghost_columns} from _gh_ost_test_gho" -ss | md5sum)
+  orig_checksum=$(gh-ost-test-mysql-replica --default-character-set=utf8mb4 test -e "select ${orig_columns} from gh_ost_test ${order_by}" -ss | md5sum)
+  ghost_checksum=$(gh-ost-test-mysql-replica --default-character-set=utf8mb4 test -e "select ${ghost_columns} from _gh_ost_test_gho ${order_by}" -ss | md5sum)
 
   if [ "$orig_checksum" != "$ghost_checksum" ] ; then
     echo "ERROR $test_name: checksum mismatch"