diff --git a/var/spack/repos/builtin/packages/petsc/package.py b/var/spack/repos/builtin/packages/petsc/package.py
index 577f53a163..6c5ab4a564 100644
--- a/var/spack/repos/builtin/packages/petsc/package.py
+++ b/var/spack/repos/builtin/packages/petsc/package.py
@@ -16,14 +16,15 @@ class Petsc(Package):
     """
 
     homepage = "http://www.mcs.anl.gov/petsc/index.html"
-    url      = "http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-3.5.3.tar.gz"
-    git      = "https://gitlab.com/petsc/petsc.git"
-
+    url = "http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-lite-3.13.0.tar.gz"
+    git = "https://gitlab.com/petsc/petsc.git"
     maintainers = ['balay', 'barrysmith', 'jedbrown']
 
     version('develop', branch='master')
     version('xsdk-0.2.0', tag='xsdk-0.2.0')
 
+    version('3.13.0', sha256='f0ea543a54145c5d1387e25b121c3fd1b1ca834032c5a33f6f1d929e95bdf0e5')
+    version('3.12.5', sha256='d676eb67e79314d6cca6422d7c477d2b192c830b89d5edc6b46934f7453bcfc0')
     version('3.12.4', sha256='56a941130da93bbacb3cfa74dcacea1e3cd8e36a0341f9ced09977b1457084c3')
     version('3.12.3', sha256='91f77d7b0f54056f085b9e27938922db3d9bb1734a2e2a6d26f43d3e6c0cf631')
     version('3.12.2', sha256='d874b2e198c4cb73551c2eca1d2c5d27da710be4d00517adb8f9eb3d6d0375e8')
@@ -146,7 +147,8 @@ class Petsc(Package):
     depends_on('metis@5:~int64', when='@3.8:+metis~int64')
     depends_on('metis@5:+int64', when='@3.8:+metis+int64')
 
-    depends_on('hdf5@:1.10.99+mpi+hl+fortran', when='+hdf5+mpi')
+    depends_on('hdf5@:1.10.99+mpi+hl+fortran', when='@:3.12.99+hdf5+mpi')
+    depends_on('hdf5+mpi+hl+fortran', when='@3.13:+hdf5+mpi')
     depends_on('zlib', when='+hdf5')
     depends_on('parmetis', when='+metis+mpi')
     depends_on('valgrind', when='+valgrind')
@@ -172,6 +174,8 @@ class Petsc(Package):
     depends_on('superlu-dist@5.4:5.4.99+int64', when='@3.10:3.10.2+superlu-dist+mpi+int64')
     depends_on('superlu-dist@6.1:6.1.99~int64', when='@3.10.3:3.12.99+superlu-dist+mpi~int64')
     depends_on('superlu-dist@6.1:6.1.99+int64', when='@3.10.3:3.12.99+superlu-dist+mpi+int64')
+    depends_on('superlu-dist@6.1:6.3.99~int64', when='@3.13.0:3.13.99+superlu-dist+mpi~int64')
+    depends_on('superlu-dist@6.1:6.3.99+int64', when='@3.13.0:3.13.99+superlu-dist+mpi+int64')
     depends_on('superlu-dist@xsdk-0.2.0~int64', when='@xsdk-0.2.0+superlu-dist+mpi~int64')
     depends_on('superlu-dist@xsdk-0.2.0+int64', when='@xsdk-0.2.0+superlu-dist+mpi+int64')
     depends_on('superlu-dist@develop~int64', when='@develop+superlu-dist+mpi~int64')
@@ -185,6 +189,13 @@ class Petsc(Package):
     depends_on('suite-sparse', when='+suite-sparse')
     depends_on('libx11', when='+X')
 
+    def url_for_version(self, version):
+        if version >= Version('3.13.0'):
+            # petsc-lite tarballs are smaller by skipping docs
+            return "http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-lite-{0}.tar.gz".format(version)
+        else:
+            return "http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-{0}.tar.gz".format(version)
+
     def mpi_dependent_options(self):
         if '~mpi' in self.spec:
             compiler_opts = [