diff --git a/src/lib/Hydra/Controller/Job.pm b/src/lib/Hydra/Controller/Job.pm
index 1b36e41f..bed362e6 100644
--- a/src/lib/Hydra/Controller/Job.pm
+++ b/src/lib/Hydra/Controller/Job.pm
@@ -82,7 +82,7 @@ sub overview : Chained('job') PathPart('') Args(0) {
     # If this is an aggregate job, then get its constituents.
     my @constituents = $c->model('DB::Builds')->search(
         { aggregate => { -in => $job->builds->search({}, { columns => ["id"], order_by => "id desc", rows => 15 })->as_query } },
-        { join => 'aggregateconstituents_constituents', 
+        { join => 'aggregateconstituents_constituents',
           columns => ['id', 'job', 'finished', 'buildstatus'],
           +select => ['aggregateconstituents_constituents.aggregate'],
           +as => ['aggregate']
@@ -99,7 +99,7 @@ sub overview : Chained('job') PathPart('') Args(0) {
 
     foreach my $agg (keys %$aggregates) {
         # FIXME: could be done in one query.
-        $aggregates->{$agg}->{build} = 
+        $aggregates->{$agg}->{build} =
             $c->model('DB::Builds')->find({id => $agg}, {columns => [@buildListColumns]}) or die;
     }
 
@@ -172,7 +172,7 @@ sub get_builds : Chained('job') PathPart('') CaptureArgs(0) {
     my ($self, $c) = @_;
     $c->stash->{allBuilds} = $c->stash->{job}->builds;
     $c->stash->{latestSucceeded} = $c->model('DB')->resultset('LatestSucceededForJob')
-        ->search({}, {bind => [$c->stash->{project}->name, $c->stash->{jobset}->name, $c->stash->{job}->name]});
+        ->search({}, {bind => [$c->stash->{jobset}->name, $c->stash->{job}->name]});
     $c->stash->{channelBaseName} =
         $c->stash->{project}->name . "-" . $c->stash->{jobset}->name . "-" . $c->stash->{job}->name;
 }
diff --git a/src/lib/Hydra/Controller/Jobset.pm b/src/lib/Hydra/Controller/Jobset.pm
index 0be73418..578b9010 100644
--- a/src/lib/Hydra/Controller/Jobset.pm
+++ b/src/lib/Hydra/Controller/Jobset.pm
@@ -162,7 +162,7 @@ sub get_builds : Chained('jobsetChain') PathPart('') CaptureArgs(0) {
     my ($self, $c) = @_;
     $c->stash->{allBuilds} = $c->stash->{jobset}->builds;
     $c->stash->{latestSucceeded} = $c->model('DB')->resultset('LatestSucceededForJobset')
-        ->search({}, {bind => [$c->stash->{project}->name, $c->stash->{jobset}->name]});
+        ->search({}, {bind => [$c->stash->{jobset}->name]});
     $c->stash->{channelBaseName} =
         $c->stash->{project}->name . "-" . $c->stash->{jobset}->name;
 }
diff --git a/src/lib/Hydra/Schema/Builds.pm b/src/lib/Hydra/Schema/Builds.pm
index 53454867..fdbc5ed6 100644
--- a/src/lib/Hydra/Schema/Builds.pm
+++ b/src/lib/Hydra/Schema/Builds.pm
@@ -68,7 +68,7 @@ __PACKAGE__->table("builds");
 
   data_type: 'integer'
   is_foreign_key: 1
-  is_nullable: 1
+  is_nullable: 0
 
 =head2 job
 
@@ -222,7 +222,7 @@ __PACKAGE__->add_columns(
   "jobset",
   { data_type => "text", is_foreign_key => 1, is_nullable => 0 },
   "jobset_id",
-  { data_type => "integer", is_foreign_key => 1, is_nullable => 1 },
+  { data_type => "integer", is_foreign_key => 1, is_nullable => 0 },
   "job",
   { data_type => "text", is_foreign_key => 1, is_nullable => 0 },
   "nixname",
@@ -466,12 +466,7 @@ __PACKAGE__->belongs_to(
   "jobset",
   "Hydra::Schema::Jobsets",
   { id => "jobset_id" },
-  {
-    is_deferrable => 0,
-    join_type     => "LEFT",
-    on_delete     => "CASCADE",
-    on_update     => "NO ACTION",
-  },
+  { is_deferrable => 0, on_delete => "CASCADE", on_update => "NO ACTION" },
 );
 
 =head2 jobset_project_jobset
@@ -578,8 +573,8 @@ __PACKAGE__->many_to_many(
 );
 
 
-# Created by DBIx::Class::Schema::Loader v0.07049 @ 2020-02-06 12:32:28
-# DO NOT MODIFY THIS OR ANYTHING ABOVE! md5sum:RvrINOAowDcde8Nd9VD6rQ
+# Created by DBIx::Class::Schema::Loader v0.07049 @ 2020-02-06 12:34:25
+# DO NOT MODIFY THIS OR ANYTHING ABOVE! md5sum:EEXlcKN/ydXJ129vT0jTUw
 
 __PACKAGE__->has_many(
   "dependents",
@@ -642,8 +637,8 @@ QUERY
 
 makeQueries('', "");
 makeQueries('ForProject', "and project = ?");
-makeQueries('ForJobset', "and project = ? and jobset = ?");
-makeQueries('ForJob', "and project = ? and jobset = ? and job = ?");
+makeQueries('ForJobset', "and jobset_id = (select id from jobsets j where j.name = ?)");
+makeQueries('ForJob', "and jobset_id = (select id from jobsets j where j.name = ?) and job = ?");
 
 
 my %hint = (
diff --git a/src/lib/Hydra/Schema/Jobs.pm b/src/lib/Hydra/Schema/Jobs.pm
index d4126e32..714497f1 100644
--- a/src/lib/Hydra/Schema/Jobs.pm
+++ b/src/lib/Hydra/Schema/Jobs.pm
@@ -51,7 +51,7 @@ __PACKAGE__->table("jobs");
 
   data_type: 'integer'
   is_foreign_key: 1
-  is_nullable: 1
+  is_nullable: 0
 
 =head2 name
 
@@ -66,7 +66,7 @@ __PACKAGE__->add_columns(
   "jobset",
   { data_type => "text", is_foreign_key => 1, is_nullable => 0 },
   "jobset_id",
-  { data_type => "integer", is_foreign_key => 1, is_nullable => 1 },
+  { data_type => "integer", is_foreign_key => 1, is_nullable => 0 },
   "name",
   { data_type => "text", is_nullable => 0 },
 );
@@ -139,12 +139,7 @@ __PACKAGE__->belongs_to(
   "jobset",
   "Hydra::Schema::Jobsets",
   { id => "jobset_id" },
-  {
-    is_deferrable => 0,
-    join_type     => "LEFT",
-    on_delete     => "CASCADE",
-    on_update     => "NO ACTION",
-  },
+  { is_deferrable => 0, on_delete => "CASCADE", on_update => "NO ACTION" },
 );
 
 =head2 jobset_project_jobset
@@ -197,7 +192,25 @@ __PACKAGE__->has_many(
 );
 
 
-# Created by DBIx::Class::Schema::Loader v0.07049 @ 2020-02-06 12:30:58
-# DO NOT MODIFY THIS OR ANYTHING ABOVE! md5sum:dFusVjxb423gIEoadAw9sw
+# Created by DBIx::Class::Schema::Loader v0.07049 @ 2020-02-06 12:33:28
+# DO NOT MODIFY THIS OR ANYTHING ABOVE! md5sum:C5Tyh8Ke4yC6q7KIFVOHcQ
+
+=head2 builds
+
+Type: has_many
+
+Related object: L<Hydra::Sc2hema::Builds>
+
+=cut
+
+__PACKAGE__->has_many(
+  "builds",
+  "Hydra::Schema::Builds",
+  {
+    "foreign.job"     => "self.name",
+    "foreign.jobset_id"  => "self.jobset_id",
+  },
+  undef,
+);
 
 1;
diff --git a/src/lib/Hydra/Schema/Jobsets.pm b/src/lib/Hydra/Schema/Jobsets.pm
index fbbb253c..572b5642 100644
--- a/src/lib/Hydra/Schema/Jobsets.pm
+++ b/src/lib/Hydra/Schema/Jobsets.pm
@@ -423,10 +423,7 @@ Related object: L<Hydra::Schema::Builds>
 __PACKAGE__->has_many(
   "builds",
   "Hydra::Schema::Builds",
-  {
-    "foreign.jobset"  => "self.name",
-    "foreign.project" => "self.project",
-  },
+  { "foreign.jobset_id" => "self.id" },
   undef,
 );
 
@@ -441,10 +438,7 @@ Related object: L<Hydra::Schema::Jobs>
 __PACKAGE__->has_many(
   "jobs",
   "Hydra::Schema::Jobs",
-  {
-    "foreign.jobset"  => "self.name",
-    "foreign.project" => "self.project",
-  },
+  { "foreign.jobset_id" => "self.id" },
   undef,
 );
 
diff --git a/src/script/hydra-eval-jobset b/src/script/hydra-eval-jobset
index b69d4b2b..9074955f 100755
--- a/src/script/hydra-eval-jobset
+++ b/src/script/hydra-eval-jobset
@@ -143,7 +143,7 @@ sub fetchInputSystemBuild {
     $jobsetName ||= $jobset->name;
 
     my @latestBuilds = $db->resultset('LatestSucceededForJob')
-        ->search({}, {bind => [$projectName, $jobsetName, $jobName]});
+        ->search({}, {bind => [$jobsetName, $jobName]});
 
     my @validBuilds = ();
     foreach my $build (@latestBuilds) {
diff --git a/src/sql/hydra.sql b/src/sql/hydra.sql
index 8349e3be..1f4288f7 100644
--- a/src/sql/hydra.sql
+++ b/src/sql/hydra.sql
@@ -146,7 +146,7 @@ create table JobsetInputAlts (
 create table Jobs (
     project       text not null,
     jobset        text not null,
-    jobset_id     integer null,
+    jobset_id     integer not null,
     name          text not null,
 
     primary key   (project, jobset, name),
@@ -170,7 +170,7 @@ create table Builds (
     -- Info about the inputs.
     project       text not null,
     jobset        text not null,
-    jobset_id     integer null,
+    jobset_id     integer not null,
     job           text not null,
 
     -- Info about the build result.
@@ -682,6 +682,7 @@ create index IndexBuildsOnProject on Builds(project);
 create index IndexBuildsOnTimestamp on Builds(timestamp);
 create index IndexBuildsOnFinishedStopTime on Builds(finished, stoptime DESC);
 create index IndexBuildsOnJobFinishedId on builds(project, jobset, job, system, finished, id DESC);
+create index IndexFinishedSuccessfulBuilds on Builds(id DESC, buildstatus, finished, job, jobset_id) where buildstatus = 0 and finished = 1;
 create index IndexBuildsOnDrvPath on Builds(drvPath);
 create index IndexCachedHgInputsOnHash on CachedHgInputs(uri, branch, sha256hash);
 create index IndexCachedGitInputsOnHash on CachedGitInputs(uri, branch, sha256hash);
diff --git a/src/sql/upgrade-63.sql b/src/sql/upgrade-63.sql
new file mode 100644
index 00000000..a7476e68
--- /dev/null
+++ b/src/sql/upgrade-63.sql
@@ -0,0 +1,7 @@
+-- Make the Jobs.jobset_id column NOT NULL. If this upgrade fails,
+-- either the admin didn't run the backfiller or there is a bug. If
+-- the admin ran the backfiller and there are null columns, it is
+-- very important to figure out where the nullable columns came from.
+
+ALTER TABLE Jobs
+  ALTER COLUMN jobset_id SET NOT NULL;
diff --git a/src/sql/upgrade-64.sql b/src/sql/upgrade-64.sql
new file mode 100644
index 00000000..76afa9e7
--- /dev/null
+++ b/src/sql/upgrade-64.sql
@@ -0,0 +1,7 @@
+-- Make the Builds.jobset_id column NOT NULL. If this upgrade fails,
+-- either the admin didn't run the backfiller or there is a bug. If
+-- the admin ran the backfiller and there are null columns, it is
+-- very important to figure out where the nullable columns came from.
+
+ALTER TABLE Builds
+  ALTER COLUMN jobset_id SET NOT NULL;
diff --git a/src/sql/upgrade-65.sql b/src/sql/upgrade-65.sql
new file mode 100644
index 00000000..05986887
--- /dev/null
+++ b/src/sql/upgrade-65.sql
@@ -0,0 +1,4 @@
+-- Index more exactly what the latest-finished query looks for.
+create index IndexFinishedSuccessfulBuilds
+  on Builds(id DESC, buildstatus, finished, job, jobset_id)
+  where buildstatus = 0 and finished = 1;