diff --git a/.Rbuildignore b/.Rbuildignore
index c5928ef14..3680560b4 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -18,3 +18,4 @@
 ^\.github$
 ^CRAN-RELEASE$
 ^data-raw$
+^minver$
diff --git a/.travis.yml b/.travis.yml
index a6d18acb0..f78fed507 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -48,10 +48,13 @@ jobs:
   - r: release
     env:
     - BUILD_PKGDOWN=true
-  - r: 3.5
-  - r: 3.4
-  - r: 3.3
   - r: 3.2
+  # old fansi needs R 3.3
+  - r: 3.3
+    env:
+    - MIN_VERSIONS=TRUE
+  - r: 3.4
+  - r: 3.5
   fast_finish: true
 
 #env
diff --git a/DESCRIPTION b/DESCRIPTION
index 936abf317..bc6c07709 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -14,18 +14,17 @@ LazyData: true
 URL: https://github.com/r-lib/pillar
 BugReports: https://github.com/r-lib/pillar/issues
 Imports: 
-    cli (>= 1.1.0),
+    cli,
     crayon (>= 1.3.4),
-    fansi (>= 0.4.0),
-    methods,
-    rlang (>= 0.3.4),
-    utf8 (>= 1.1.4),
-    vctrs (>= 0.1.0)
+    fansi,
+    rlang (>= 0.3.0),
+    utf8 (>= 1.1.0),
+    vctrs
 Suggests: 
-    knitr (>= 1.22),
-    lubridate (>= 1.7.4),
-    testthat (>= 2.1.1),
-    withr (>= 2.1.2)
+    knitr,
+    lubridate,
+    testthat,
+    withr
 Roxygen: list(markdown = TRUE)
 RoxygenNote: 6.1.1
 Collate: 
diff --git a/minver/.gitignore b/minver/.gitignore
new file mode 100644
index 000000000..ea92e9fc9
--- /dev/null
+++ b/minver/.gitignore
@@ -0,0 +1,2 @@
+*.rds
+lib/
diff --git a/minver/01-gen.R b/minver/01-gen.R
new file mode 100644
index 000000000..5a4216c83
--- /dev/null
+++ b/minver/01-gen.R
@@ -0,0 +1,20 @@
+library(tidyverse)
+
+# pkgdep <- pkgdep::as_pkgdep(available.packages())
+# gen <- pkgdep::get_all_deps("tibble", pkgdep)
+
+my_package <- basename(getwd())
+
+db <- cranly::clean_CRAN_db()
+network <- cranly::build_network(db)
+tree <- cranly::compute_dependence_tree(network, my_package)
+
+deps <- desc::desc_get_deps()
+
+tree %>%
+  arrange(generation) %>%
+  distinct(package, .keep_all = TRUE) %>%
+  arrange(-generation) %>%
+  inner_join(deps, by = "package") %>%
+  filter(version != "*") %>%
+  saveRDS("minver/gen.rds")
diff --git a/minver/02-baseline.R b/minver/02-baseline.R
new file mode 100644
index 000000000..c484a6e7c
--- /dev/null
+++ b/minver/02-baseline.R
@@ -0,0 +1,18 @@
+library(tidyverse)
+
+gen <-
+  readRDS("minver/gen.rds") %>%
+  as_tibble()
+
+gen_crandb <-
+  gen %>%
+  select(-type, -version) %>%
+  mutate(crandb = map(package, ~ crandb::package(., version = "all")))
+
+baseline <-
+  gen_crandb %>%
+  mutate(version = map(crandb, ~ names(pluck(., "versions")))) %>%
+  mutate(first_version = map_chr(version, 1)) %>%
+  select(-crandb)
+
+saveRDS(baseline, "minver/baseline.rds")
diff --git a/minver/03-candidate.R b/minver/03-candidate.R
new file mode 100644
index 000000000..8c711c0fe
--- /dev/null
+++ b/minver/03-candidate.R
@@ -0,0 +1,9 @@
+library(tidyverse)
+
+baseline <- readRDS("minver/baseline.rds")
+
+baseline %>%
+  select(package = 1) %>%
+  pwalk(desc::desc_set_dep)
+
+saveRDS(baseline, "minver/candidate-0001.rds")
diff --git a/minver/04-lib.R b/minver/04-lib.R
new file mode 100644
index 000000000..a8774351f
--- /dev/null
+++ b/minver/04-lib.R
@@ -0,0 +1,9 @@
+library(tidyverse)
+
+lib <- "minver/lib"
+unlink(lib, recursive = TRUE, force = TRUE)
+dir.create(lib, showWarnings = FALSE)
+
+invisible(remotes::install_deps)
+withr::with_libpaths(lib, remotes::install_deps(dependencies = TRUE))
+withr::with_libpaths(lib, install.packages("memoise"))
diff --git a/minver/05-next-candidate.R b/minver/05-next-candidate.R
new file mode 100644
index 000000000..a6d14aa06
--- /dev/null
+++ b/minver/05-next-candidate.R
@@ -0,0 +1,90 @@
+library(tidyverse)
+
+bisect_first_min_version <- function(version) {
+  na_versions <- which(map_int(version, length) > 1)
+  if (length(na_versions) == 0) stop("All versions determined, move to next script.", call. = FALSE)
+  first_na_version <- na_versions[[1]]
+
+  version_candidates <- version[[first_na_version]]
+
+  version_idx <- quantile(seq_along(version_candidates), 0.5, type = 1)
+
+  min_version <- rep(NA_character_, length(version))
+
+  pinned <- seq_len(first_na_version - 1)
+  min_version[pinned] <- unlist(version[pinned])
+  min_version[[first_na_version]] <- version_candidates[[version_idx]]
+  min_version
+}
+
+update_bisect_result <- function(version, next_min_version, failure) {
+  first_na_version <- which(map_int(version, length) > 1)[[1]]
+
+  version_candidates <- package_version(version[[first_na_version]])
+  pivot <- package_version(next_min_version[[first_na_version]])
+
+  if (failure) {
+    version_candidates <- version_candidates[ version_candidates > pivot ]
+  } else {
+    version_candidates <- version_candidates[ version_candidates <= pivot ]
+  }
+
+  version[[first_na_version]] <- as.character(version_candidates)
+  version
+}
+
+candidate_files <- dir("minver", pattern = "candidate-....[.]rds")
+
+candidate_file <- tail(candidate_files, 1)[[1]]
+
+candidate <-
+  readRDS(file.path("minver", candidate_file)) %>%
+  mutate(next_min_version = bisect_first_min_version(version)) %>%
+  mutate(dep = if_else(is.na(next_min_version), "*", paste0(">= ", next_min_version)))
+
+print(candidate)
+
+pinned <-
+  candidate %>%
+  filter(!is.na(next_min_version)) %>%
+  select(package = 1, version = next_min_version) %>%
+  arrange(-row_number())
+
+print(pinned)
+
+libpath <- tempfile("lib")
+dir.create(libpath)
+
+existing <- setdiff(dir("minver/lib"), pinned$package)
+
+stopifnot(all(file.symlink(normalizePath(file.path("minver/lib", existing)), libpath)))
+
+invisible(remotes::install_version)
+invisible(rcmdcheck::rcmdcheck)
+
+Sys.setenv(NOT_CRAN = "true")
+
+result <- safely(
+  ~ withr::with_libpaths(
+    libpath,
+    {
+      pwalk(pinned, remotes::install_version, dependencies = character(), upgrade = "never")
+      rcmdcheck::rcmdcheck(error_on = "note")
+    }
+  )
+)()
+
+failure <- is.null(result$result)
+failure
+
+n <- length(candidate_files) + 1
+
+new_candidate <-
+  candidate %>%
+  mutate(version = update_bisect_result(version, next_min_version, failure)) %>%
+  select(-next_min_version, -dep)
+
+new_candidate %>%
+  saveRDS(sprintf("minver/candidate-%.4d.rds", n))
+
+new_candidate
diff --git a/minver/06-finalize.R b/minver/06-finalize.R
new file mode 100644
index 000000000..d083922cd
--- /dev/null
+++ b/minver/06-finalize.R
@@ -0,0 +1,13 @@
+library(tidyverse)
+
+candidate_files <- dir("minver", pattern = "candidate-....[.]rds")
+
+candidate_file <- tail(candidate_files, 1)[[1]]
+
+final <-
+  readRDS(file.path("minver", candidate_file)) %>%
+  unnest() %>%
+  mutate(cond = if_else(version == first_version, "*", paste0(">= ", version))) %>%
+  select(package, version = cond)
+
+pwalk(final, desc::desc_set_dep)
diff --git a/minver/README.md b/minver/README.md
new file mode 100644
index 000000000..f891ce83e
--- /dev/null
+++ b/minver/README.md
@@ -0,0 +1,26 @@
+# minver
+
+A workflow for finding the minimum required versions of all packages.
+
+## How does it work?
+
+1. It creates a baseline library via `remotes::install_deps(dependencies = TRUE)` .
+
+2. Imported packages are sorted topologically, packages that depend on other packages come first. Versions are erased from the `DESCRIPTION` .
+
+3. For each imported package, a bisection along the available versions (obtained via `crandb::package(version = "all")`) is made. The baseline library is copied (using symlinks), and the packages for which minimum versions are to be tested are installed using `remotes::install_version()`. The test criterion is a successful `R CMD check` without NOTEs.
+
+4. The minimum version for each package is written to the `DESCRIPTION` .
+
+## Run it
+
+Copy the `minver` directory into the root of your package, call `usethis::use_build_ignore("minver")`.
+
+Run each script `??-*.R` in sequence, the `05-*.R` script must be run repeatedly until the error `"All versions determined, move to next script."` is raised.
+
+The following files are created:
+
+- `gen.rds`: Imported packages sorted by "generation" (topologically)
+- `baseline.rds`: All CRAN versions of imported packages
+- `lib/`: The baseline library
+- `candidate-####.rds`: Intermediate results of the bisection
diff --git a/tic.R b/tic.R
index 1e575d9dc..04d31bacf 100644
--- a/tic.R
+++ b/tic.R
@@ -3,6 +3,34 @@ do_package_checks()
 if (ci_has_env("DEV_VERSIONS")) {
   get_stage("install") %>%
     add_step(step_install_github(c("r-lib/rlang", "r-lib/cli", "r-lib/crayon", "brodieG/fansi", "patperry/r-utf8", "r-lib/vctrs")))
+} else if (ci_has_env("MIN_VERSIONS")) {
+  # Make sure all other packages are installed when we downgrade
+  get_stage("before_script") %>%
+    add_code_step(
+      {
+        deps <- desc::desc_get_deps()
+        deps <- deps[deps$type == "Imports", ]
+
+        # revdepcheck needs recent cli, installing in the same library
+        deps <- deps[deps$package != "cli", ]
+
+        is_first <- (deps$version == "*")
+        all_first_packages <- lapply(deps$package[is_first], crandb::package, version = "all")
+        all_first_version_details <- lapply(all_first_packages, `[[`, "versions")
+        all_first_versions <- lapply(all_first_version_details, names)
+        first_versions <- vapply(all_first_versions, `[[`, 1, FUN.VALUE = character(1))
+
+        version <- rlang::rep_along(NA_character_, is_first)
+        version[is_first] <- first_versions
+        version[!is_first] <- gsub(">= ", "", deps$version[!is_first])
+
+        Map(remotes::install_version, deps$package, version)
+      },
+      {
+        remotes::install_cran("desc")
+        remotes::install_github("r-hub/crandb")
+      }
+    )
 }
 
 if (ci_has_env("BUILD_PKGDOWN") && ci_get_branch() == "master") {