diff --git a/addons/product/models/product_pricelist.py b/addons/product/models/product_pricelist.py
index 6ca1a827927..61d3feff07a 100644
--- a/addons/product/models/product_pricelist.py
+++ b/addons/product/models/product_pricelist.py
@@ -314,34 +314,53 @@ class Pricelist(models.Model):
         res = self._get_partner_pricelist_multi([partner_id], company_id)
         return res[partner_id].id
 
+    def _get_partner_pricelist_multi_search_domain_hook(self):
+        return []
+
+    def _get_partner_pricelist_multi_filter_hook(self):
+        return self
+
     def _get_partner_pricelist_multi(self, partner_ids, company_id=None):
         """ Retrieve the applicable pricelist for given partners in a given company.
 
+            It will return the first found pricelist in this order:
+            First, the pricelist of the specific property (res_id set), this one
+                   is created when saving a pricelist on the partner form view.
+            Else, it will return the pricelist of the partner country group
+            Else, it will return the generic property (res_id not set), this one
+                  is created on the company creation.
+            Else, it will return the first available pricelist
+
             :param company_id: if passed, used for looking up properties,
                 instead of current user's company
             :return: a dict {partner_id: pricelist}
         """
-        Partner = self.env['res.partner']
+        # `partner_ids` might be ID from inactive uers. We should use active_test
+        # as we will do a search() later (real case for website public user).
+        Partner = self.env['res.partner'].with_context(active_test=False)
+
         Property = self.env['ir.property'].with_context(force_company=company_id or self.env.user.company_id.id)
         Pricelist = self.env['product.pricelist']
+        pl_domain = self._get_partner_pricelist_multi_search_domain_hook()
 
-        # retrieve values of property
+        # if no specific property, try to find a fitting pricelist
         result = Property.get_multi('property_product_pricelist', Partner._name, partner_ids)
 
-        remaining_partner_ids = [pid for pid, val in result.items() if not val]
+        remaining_partner_ids = [pid for pid, val in result.items() if not val or
+                                 not val._get_partner_pricelist_multi_filter_hook()]
         if remaining_partner_ids:
             # get fallback pricelist when no pricelist for a given country
             pl_fallback = (
-                Pricelist.search([('country_group_ids', '=', False)], limit=1) or
+                Pricelist.search(pl_domain + [('country_group_ids', '=', False)], limit=1) or
                 Property.get('property_product_pricelist', 'res.partner') or
-                Pricelist.search([], limit=1)
+                Pricelist.search(pl_domain, limit=1)
             )
             # group partners by country, and find a pricelist for each country
             domain = [('id', 'in', remaining_partner_ids)]
             groups = Partner.read_group(domain, ['country_id'], ['country_id'])
             for group in groups:
                 country_id = group['country_id'] and group['country_id'][0]
-                pl = Pricelist.search([('country_group_ids.country_ids', '=', country_id)], limit=1)
+                pl = Pricelist.search(pl_domain + [('country_group_ids.country_ids', '=', country_id)], limit=1)
                 pl = pl or pl_fallback
                 for pid in Partner.search(group['__domain']).ids:
                     result[pid] = pl
diff --git a/addons/website_sale/data/data.xml b/addons/website_sale/data/data.xml
index 81639c17cd0..ce716bebba9 100644
--- a/addons/website_sale/data/data.xml
+++ b/addons/website_sale/data/data.xml
@@ -40,7 +40,7 @@
 
         <record model="product.pricelist" id="product.list0">
             <field name="selectable" eval="False" />
-            <field name="website_id" ref="website.default_website" />
+            <field name="website_id" eval="False"/>
         </record>
     </data>
     <data>
diff --git a/addons/website_sale/data/demo.xml b/addons/website_sale/data/demo.xml
index 97217d3d11a..25f03e0f915 100644
--- a/addons/website_sale/data/demo.xml
+++ b/addons/website_sale/data/demo.xml
@@ -224,7 +224,6 @@
 
         <record model="product.pricelist" id="product.list0">
             <field name="selectable" eval="True" />
-            <field name="website_id" ref="website.default_website" />
             <field name="sequence">3</field>
             <field name="currency_id" ref="base.USD"/>
         </record>
diff --git a/addons/website_sale/models/product.py b/addons/website_sale/models/product.py
index 5bc579637e6..d9c421e76b9 100644
--- a/addons/website_sale/models/product.py
+++ b/addons/website_sale/models/product.py
@@ -2,6 +2,7 @@
 # Part of Odoo. See LICENSE file for full copyright and licensing details.
 from odoo import api, fields, models, tools, _
 from odoo.addons import decimal_precision as dp
+from odoo.addons.website.models import ir_http
 from odoo.tools.translate import html_translate
 
 
@@ -17,9 +18,12 @@ class ProductPricelist(models.Model):
     _inherit = "product.pricelist"
 
     def _default_website(self):
-        return self.env['website'].search([], limit=1)
+        """ Find the first company's website, if there is one. """
+        company_id = self.env.user.company_id.id
+        domain = [('company_id', '=', company_id)]
+        return self.env['website'].search(domain, limit=1)
 
-    website_id = fields.Many2one('website', string="website", default=_default_website)
+    website_id = fields.Many2one('website', string="Website", default=_default_website)
     code = fields.Char(string='E-commerce Promotional Code', groups="base.group_user")
     selectable = fields.Boolean(help="Allow the end user to choose this price list")
 
@@ -48,6 +52,45 @@ class ProductPricelist(models.Model):
         self.clear_cache()
         return res
 
+    def _get_partner_pricelist_multi_search_domain_hook(self):
+        domain = super(ProductPricelist, self)._get_partner_pricelist_multi_search_domain_hook()
+        website = ir_http.get_request_website()
+        if website:
+            domain += self._get_website_pricelists_domain(website.id)
+        return domain
+
+    def _get_partner_pricelist_multi_filter_hook(self):
+        res = super(ProductPricelist, self)._get_partner_pricelist_multi_filter_hook()
+        website = ir_http.get_request_website()
+        if website:
+            res = res.filtered(lambda pl: pl._is_available_on_website(website.id))
+        return res
+
+    @api.multi
+    def _is_available_on_website(self, website_id):
+        """ To be able to be used on a website, a pricelist should either:
+        - Have its `website_id` set to current website (specific pricelist).
+        - Have no `website_id` set and should be `selectable` (generic pricelist)
+          or should have a `code` (generic promotion).
+
+        Note: A pricelist without a website_id, not selectable and without a
+              code is a backend pricelist.
+
+        Change in this method should be reflected in `_get_website_pricelists_domain`.
+        """
+        self.ensure_one()
+        return self.website_id.id == website_id or (not self.website_id and (self.selectable or self.code))
+
+    def _get_website_pricelists_domain(self, website_id):
+        ''' Check above `_is_available_on_website` for explanation.
+        Change in this method should be reflected in `_is_available_on_website`.
+        '''
+        return [
+            '|', ('website_id', '=', website_id),
+            '&', ('website_id', '=', False),
+            '|', ('selectable', '=', True), ('code', '!=', False),
+        ]
+
 
 class ProductPublicCategory(models.Model):
     _name = "product.public.category"
diff --git a/addons/website_sale/models/website.py b/addons/website_sale/models/website.py
index 0f57030c95a..c781f36d977 100644
--- a/addons/website_sale/models/website.py
+++ b/addons/website_sale/models/website.py
@@ -32,7 +32,12 @@ class Website(models.Model):
 
     @api.one
     def _compute_pricelist_ids(self):
-        self.pricelist_ids = self.env["product.pricelist"].search([("website_id", "=", self.id)])
+        """ Return the pricelists that can be used directly or indirectly on
+        the website.
+        """
+        Pricelist = self.env["product.pricelist"]
+        domain = Pricelist._get_website_pricelists_domain(self.id)
+        self.pricelist_ids = Pricelist.search(domain)
 
     @api.multi
     def _compute_pricelist_id(self):
@@ -66,8 +71,8 @@ class Website(models.Model):
         partner = self.env.user.partner_id
         is_public = self.user_id.id == self.env.user.id
         if not is_public and (not pricelists or (partner_pl or partner.property_product_pricelist.id) != website_pl):
-            if partner.property_product_pricelist.website_id:
-                pricelists |= partner.property_product_pricelist
+            # `property_product_pricelist` is already multi-website compliant
+            pricelists |= partner.property_product_pricelist
 
         if not pricelists:  # no pricelist for this country, or no GeoIP
             pricelists |= all_pl.filtered(lambda pl: not show_visible or pl.selectable or pl.id in (current_pl, order_pl))
@@ -75,7 +80,7 @@ class Website(models.Model):
             pricelists |= all_pl.filtered(lambda pl: pl.sudo().code)
 
         # This method is cached, must not return records! See also #8795
-        return pricelists.ids
+        return pricelists.filtered(lambda pl: pl._is_available_on_website(self.id)).ids
 
     # DEPRECATED (Not used anymore) -> Remove me in master (saas12.3)
     def _get_pl(self, country_code, show_visible, website_pl, current_pl, all_pl):
diff --git a/addons/website_sale/views/product_views.xml b/addons/website_sale/views/product_views.xml
index 52b57be8deb..b1503c4d8ff 100644
--- a/addons/website_sale/views/product_views.xml
+++ b/addons/website_sale/views/product_views.xml
@@ -200,7 +200,7 @@
         <field name="arch" type="xml">
             <field name='currency_id' position='after'>
                 <field name="selectable"/>
-                <field name="website_id" options="{'no_create': True}" string="Allow to use on " placeholder="None website"/>
+                <field name="website_id" options="{'no_create': True}" />
             </field>
         </field>
     </record>