diff --git a/Project.toml b/Project.toml
index 42b9806..4e6a8a4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -35,8 +35,8 @@ IncompleteLU = "40713840-3770-5561-ab4c-a76e7d0d7895"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
 ODEProblemLibrary = "fdc4e326-1af4-4b90-96e7-779fcce2daa5"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
-SparsityTracing = "06eadbd4-12ad-4cbc-ab6e-10f8370940a5"
+SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "AlgebraicMultigrid", "DiffEqCallbacks", "ODEProblemLibrary", "DAEProblemLibrary", "ForwardDiff", "SparseDiffTools", "SparsityTracing", "IncompleteLU", "ModelingToolkit"]
+test = ["Test", "AlgebraicMultigrid", "DiffEqCallbacks", "ODEProblemLibrary", "DAEProblemLibrary", "ForwardDiff", "SparseDiffTools", "SparseConnectivityTracer", "IncompleteLU", "ModelingToolkit"]
diff --git a/src/common_interface/solve.jl b/src/common_interface/solve.jl
index 004fbdd..a1cb3c0 100644
--- a/src/common_interface/solve.jl
+++ b/src/common_interface/solve.jl
@@ -483,8 +483,12 @@ function DiffEqBase.__init(prob::DiffEqBase.AbstractODEProblem{uType, tupType, i
     save_everystep = isempty(saveat), save_idxs = nothing,
     dense = save_everystep,
     save_on = true,
-    save_start = true,
-    save_end = true,
+    save_start = save_everystep || isempty(saveat) ||
+                     saveat isa Number ? true :
+                 prob.tspan[1] in saveat,
+    save_end = save_everystep || isempty(saveat) ||
+                   saveat isa Number ? true :
+               prob.tspan[2] in saveat,
     save_timeseries = nothing,
     progress = false,
     progress_steps = 1000,
@@ -1415,7 +1419,7 @@ function DiffEqBase.solve!(integrator::AbstractSundialsIntegrator; early_free =
             integrator.userfun.p = integrator.p
             solver_step(integrator, tstop)
             integrator.t = first(integrator.tout)
-            # NB: CVode, ARKode may warn and then recover if integrator.t == integrator.tprev so don't flag this as an error 
+            # NB: CVode, ARKode may warn and then recover if integrator.t == integrator.tprev so don't flag this as an error
             integrator.flag < 0 && break
             handle_callbacks!(integrator) # this also updates the interpolation
             integrator.flag < 0 && break
diff --git a/test/common_interface/arkode.jl b/test/common_interface/arkode.jl
index b303bc9..1b6c7b4 100644
--- a/test/common_interface/arkode.jl
+++ b/test/common_interface/arkode.jl
@@ -56,3 +56,7 @@ method = ARKODE(Sundials.Explicit();
 # Solve
 sol = solve(prob, method)
 @test sol.retcode == ReturnCode.Success
+
+#test that save_start and save_end are false by default when saveat is set
+sol = solve(prob, ARKODE(), saveat = [0.1, 0.2])
+@test sol.t == [0.1, 0.2]
diff --git a/test/common_interface/cvode.jl b/test/common_interface/cvode.jl
index a40996c..a7b1e72 100644
--- a/test/common_interface/cvode.jl
+++ b/test/common_interface/cvode.jl
@@ -46,7 +46,7 @@ sol = solve(prob, CVODE_Adams(); saveat = saveat, save_everystep = false)
 @test sol.t == saveat
 
 for tstops in [0.9, [0.9]]
-    sol = solve(prob,  CVODE_Adams(); tstops)
+    local sol = solve(prob,  CVODE_Adams(); tstops)
     @test 0.9 ∈ sol.t
 end
 
@@ -57,7 +57,7 @@ sol_idxs = solve(prob, CVODE_Adams(); save_idxs = [1], timeseries_errors = false
 
 sol_idxs = solve(prob, CVODE_Adams(); save_idxs = [1, 2], timeseries_errors = false,
     calculate_error = false)
-@test length(sol_idxs[1]) == 2
+@test length(sol_idxs[:, 1]) == 2
 @test sol[1, :] == sol_idxs[1, :]
 @test sol[2, :] == sol_idxs[2, :]
 
diff --git a/test/common_interface/ida.jl b/test/common_interface/ida.jl
index 7932c28..503e3ec 100644
--- a/test/common_interface/ida.jl
+++ b/test/common_interface/ida.jl
@@ -60,7 +60,7 @@ sol = solve(prob, IDA(); saveat = saveat, save_everystep = true)
 @test intersect(sol.t, saveat) == saveat
 @info "IDA with tstops"
 for tstops in [0.9, [0.9]]
-    sol = solve(prob, IDA(); tstops)
+    local sol = solve(prob, IDA(); tstops)
     @test 0.9 ∈ sol.t
 end
 
diff --git a/test/common_interface/jacobians.jl b/test/common_interface/jacobians.jl
index 482f174..29f358b 100644
--- a/test/common_interface/jacobians.jl
+++ b/test/common_interface/jacobians.jl
@@ -35,8 +35,7 @@ sol9 = solve(prob, CVODE_BDF(; linear_solver = :KLU))
 @test Array(sol9) ≈ Array(good_sol)
 
 Lotka_fj = ODEFunction(Lotka;
-    jac_prototype = JacVec((du, u) -> Lotka(du, u, (), 0.0), ones(2),
-        SciMLBase.NullParameters()))
+    jac_prototype = JacVec(Lotka, ones(2), SciMLBase.NullParameters(), 0.0))
 
 prob = ODEProblem(Lotka_fj, ones(2), (0.0, 10.0))
 sol9 = solve(prob, CVODE_BDF(; linear_solver = :GMRES), saveat = 0.1, abstol = 1e-12,
diff --git a/test/common_interface/precs.jl b/test/common_interface/precs.jl
index 487ef66..058c444 100644
--- a/test/common_interface/precs.jl
+++ b/test/common_interface/precs.jl
@@ -1,6 +1,6 @@
 using Sundials, Test, LinearAlgebra, IncompleteLU
 import AlgebraicMultigrid
-import SparsityTracing, SparseDiffTools
+import SparseConnectivityTracer, SparseDiffTools
 
 const N = 32
 const xyd_brusselator = range(0; stop = 1, length = N)
@@ -46,15 +46,14 @@ function init_brusselator_2d(xyd)
     u
 end
 u0 = vec(init_brusselator_2d(xyd_brusselator))
+du = similar(u0)
 
 prob_ode_brusselator_2d = ODEProblem(brusselator_2d_vec,
     u0, (0.0, 11.5), p)
 
-# find Jacobian sparsity pattern
-u0_st = SparsityTracing.create_advec(u0)
-du_st = similar(u0_st)
-brusselator_2d_vec(du_st, u0_st, p, 0.0)
-const jaccache = SparsityTracing.jacobian(du_st, length(du_st))
+detector =  SparseConnectivityTracer.TracerSparsityDetector()
+brus_uf = (du, u)->brusselator_2d_vec(du, u, p, 0.1)
+const jaccache = similar(SparseConnectivityTracer.jacobian_sparsity(brus_uf, du, u0, detector), Float64)
 const W = I - 1.0 * jaccache
 
 # setup sparse AD for Jacobian